I am able to claim an education credit but I didn't finish out the semester. am I still allowed to claim in on the taxes?

Yes.  You can claim the amounts you paid for tuition (and books) even when the student withdraws from classes if these tuition amounts were not refunded to you.  

For more information, please see:  IRS Publication 970

Even if it was paid for by the state? I qualified for state assistance so I didn’t actually pay for anything out of pocket.

That's great!  It does have to be money that you actually paid or got a loan to pay.