Dude. They were paying you as W2. You were filing your taxes.
The onus of collecting and paying withholding is on your employer unless you signed contractor paperwork at some point.

All I will say is, a company that hires employees is supposed to withhold taxes and pay in trust fund taxes.  OP isn't in any trouble here.

Provided he can substantiate his wages for the periods in question, to get full credit for Social Security.

OP needs to pull transcripts of his tax returns soonest.
OP, did you have any reason for wages on your 1040 to be less than wages taxed for Social Security? (for example, 401k contributions)

https://www.irs.gov/individuals/get-transcript
You can also request a transcript by mail by calling our automated phone transcript service at 800-908-9946.