Root canal

I thought to have my tooth extracted as it’s in the back and later replaced with an implant from my cities dental school. I’m very conflicted. I have some pain but it’s manageable. Very slight swelling to the point that most can’t tell. I can’t really afford to have a root canal done my original provider. I’ve been working on getting in with the dental school but with everyone just graduating they won’t have students back in till June 3rd. My question is since I’m on amoxicillin for infection, could I get away with waiting the few weeks to be seen at the school and do a price I can afford for a root canal ?

I know there are payment options. That just is really really difficult for me to do. I already have payment plans for medical bills and the debt overwhelms me, but I would hate for things to get so bad that I rack up medical bills or whatever else just because I delayed this for too long.