OP,  I will talk around improving your soil below, but re the triple 13:  Are you talking about a measuring cup?  or a big solo cup?   If the smaller measurement, you're not going to burn anything the way you are doing it.  It's just always a good practice to keep the fertilizer OFF of the plant itself.  You are doing it right.  

** The reason you have to reapply later is that nitrogen (the first number on the bag) leaches out of the root zone very quickly.  Usually, the other two elements (Nitrogen, Phosphorus and Potassium (N, P, K) ) do not.  At some point, a soil test might benefit you, so you know what you actually need, instead of potentially wasting product (and the money you spend on it, which I realize may be a small amount, depending on the size of the garden).

The cottonseed meal is a good choice, however it does lower soil pH.  Depending on the pH of your existing soil, you want to be aware of what any additions will do.  Another reason to soil test, if you haven't.

Now....
If you're going to improve your soil over time, you need compost--an organic addition to the soil that builds soil structure over time.  That can be a cover crop that you dig back in, like a green manure, or it can be compost you add.

****BE VERY, VERY CAREFUL WITH BUYING COMPOST.  KNOW YOUR SOURCE, TRUST YOUR SOURCE.  A LOT OF COMPOST IS LACED WITH LONG-RESIDUAL HERBICIDE THAT WILL DESTROY YOUR GARDEN SPOT FOR A LONG, LONG TIME.*****

Now then, assuming you can find a good source that you trust (or make your own, if your garden is small enough that you can) the REASON you want to use something like compost (or manure or other natural material) is that natural materials do a number of good things for your soil.  

The BIGGEST gift they give soil is to improve the soil structure.  As they break down, they create space in soil (for air--your plant roots and lots of microorganisms need to breathe) and that space also includes little caves and cavities in the soil for microbes to hang out, AND...

Now here goes a ridiculously oversimplified explanation of the chemistry.  I'm in a hurry and haven't had nearly enough coffee today, so.... Feel free to skip  ahead to "in short" below:

Your soil has stuff in it that is good stuff for your plants, but that stuff is not available--the plants can't get it.  That's cuz of the pH and/or the soil lacks the humic substances to "hold" the good stuff in a way that it can also let go of the good stuff so the plants can have it.  Most of these reactions happen because positive and negative charges attract....(so this is the poles of a battery, but tiny and in the soil)


Compost provides lots of what I call "Good Soil Juice" --that's material that allows chemical reactions to take place--basically as the compost breaks down into humus (that's one of the smallest particles of good stuff in a soil biome) it provides the different electrical points (positive and negative) and that means ALSO, it provides lots of points for different mineral elements-- (all mineral elements have charge--positive or negative) to grab onto so they can release from soil particles and become available for plant roots to actually grab.

Why is pH so important?  Because pH is Potential Hydrogen.  It's a measure (in part) of how likely the soil is, to be able to provide a Hydrogen atom when it's needed, to get, say, an atom of iron to let go of that little coloid of clay, so the plant can have the iron..  That's just one tiny example of how millions of these little positive-negative reactions happen in soil constantly.  A lot of it depends on the POTENTIAL Hydrogen... (Sorry, chemists. I'm a rotten explainer of this stuff)  

*Deep Breath...that awkward explanation is done.

Y'all who also know this stuff, feel free to elaborate because I probably need to spend some time on a write up for understanding of all this, but other folks may do a better job.


SOOOO....

In the short term, I recommend getting some humic acid based products because Humic Acid  is (don't glaze over here) a polyelectrolitic, micromolecular compound.   It's a short carbon chain structure that has a LOT of negative and positive charges hanging onto the edges of it. Get one that's made from Leonardite shale. As a liquid, it's easy to apply, will never hurt your plants, and will help the stuff you are already adding to your garden, be more available and more effective.  

I have sources I like, just because I use and trust those, but there are other sources available.  

***Another option is to also use a fertilizer that has an organic component.  Like Earthworks.  It's made of chicken poo.  Or some kind of product that has biochar as its bulk component. So you are adding  carbon to the soil as you are also adding nutrients for your plants.  The Andersons has these.  They are expensive.  Earthworks has these.  Not expensive at all for what you get from it, IMO.  I pay $30 for a (50?) lb bag of Earthworks 8-2-2.  It's an awesome fert.

Okay I've probably opened a bunch of cans of worms here, cuz I'm moving fast, I've likely confused people, and I may have started things then not finished cuz....it's Kitties, so no shocker.

**A thing to understand for everyone (not just OP cuz he/she is using an organic compound already, along with synthetic fert) is that year after year of using only synthetic fertilizers actually mines the soil of its ability to hold onto nutrients, and its ability to function as an ecosystem.  It breaks it down and damages it.  We don't want that.  Ain't sayin don't use any synthetics!  Sayin put some carbon and good stuff in there too.

In short:

1-Get a soil test so you know where you stand AND so you know the pH of your soil.

2-Include some kind of carbon EVERY TIME you apply anything.  Humic is a good place to start.  Biochar is a good place to start.

3. DO NOT do the same thing every time.   Too much of any one thing can overload soil.

4-Strive to do it the way God does it.  Plants grow.  Their roots die back and more grow.  Those dead roots break down, put carbon into the soil, and build good soil structure.  More roots grow, bigger and BETTER, cuz soil gets better each time.  More roots die back and break down.  More carbon. More humus.  Rinse and repeat.  We can do that too. Sort of.  We should all try.


I hope there is something in here that is at least helpful.

Are you asking about ways to spread interest in self sufficiency here on the forum?

There are some great tests that are less expensive.

I use Spectrum Analytic for all of my clients.  They're wonderful, I get what I need, and if I have any trouble they are right there.   Spectrum's site is not the most user-friendly but if I can figure it out, pretty much anybody can. (Kitties is not techy.)

ETA: I forgot to say, the complete soil test that I do for clients is about $40-45.   This includes micros, which a lot of tests do not.   Here is an interview (not the greatest video) with Mike from Spectrum.  He has helped me a lot with some troubled lawns. Great guy.    John Perry with Mike from Spectrum Analytic


There's another good one I can't think of right now.  I will remember and I'll edit when my brain comes online.


Finally my brain spit it out.  Ward Labs  Looks like theirs is cheaper but I have never used it and don't know what all it shows.  Details at that link though.

I have a good friend who uses Waypoint!  He really likes it, and the tests he's shown me look plenty thorough.

I haven't tried them so I can't speak to compare them to Spectrum, but a lot of test viability depends on the care taken pulling the sample.  

I know he is VERY careful to get roots and thatch out of it --which is what you should do. (This is a turfgrass friend).  Wouldn't be thatch type crap in it with garden soil unless you've tilled in a green manure crop or mulched or some such.