IF u r full time grad student means u r in f1?

Don’t worry won’t b issue . It might take time tho

If you are still maintaining F1 status while on TPS, then that means your F1 is still valid. No need to COS.

@Hanumanji: Most likely your F1 is still good. Just call USCIS, explain your situation and ask them if you need to do anything.
I called them last year because I was in a similar confusing situation, but in my case the question was whether my TPS was still valid or not.
Make sure you note down the name of the person you talk to.

"After that it is just TPS. It did not go parallel."
This suggest that's you likely fell out if status, but hold onto TPS. You can check your status using your i94 record, but it maynot be updated.
Even if you called uscis or a lawyer there will be people who will say that your are f1 vs not f1.
I suggest filing COS, AP. If you are granted COS continue inside us, else get outside the country on AP, get visa f1 interview and get inside USA again.
Just my two cents but I am not a lawyer.