I filed my 2022 tax return a few weeks ago. My company just sent me a 1095-C form. Do I need to file this form or change my tax return in any way for the 1095-C form ?

No, Form 1095-C is not entered on the return. It is proof for your records that you were covered by health insurance. 

No you don't need to enter a 1095B or 1095C on your return.  Did you say you had Health Ins when you filled out your return?  You only report a 1095A if you had Marketplace insurance (Obamacare)