628 Credit Score, lease ends in April.

Currently have $3,540 of CC debt (96% util) and 2k on a personal loan. student loans currently in forbearance, 13k left on my car. I lastly am paying off a $240 medical bill. So with around $2k in current expenses I make $2600 a month and have a cosigner.

I was wondering if paying off my high interest/low balance CC ($596) would that bump up my score to a 650 by march/april? I would probably end up using it again but I should have 2k in my moving fund by the time I have to sign a lease (not including first months rent).

I am either planning to get a studio-1 bedroom or lease by the room so budget is 550-1000 (that's a push IK) Located in NorCal for those who might try to who wonder why my rent might be cheaper than in your area.