Hiiiiiii.

Recently bought an 91 integra to fix up for fun, having some minor/annoying problems with the car however. Whenever I need to fuel the car up, it will not start again for like, 5mins with the key in the run position. The fuel cap has a fair amount of pressure behind it when attempting to remove it. As soon as I go to start it after finishing up, it runs for maybe 10seconds then completely dies for several minutes. Pumping the gas pedal doesn't help at all... So I'm puzzled... Could it just be my fuel pump? Or something else since the pump was replaced just before I bought the car according to receipts.

Pleeease help, thanks in advance. :)

If the Check Engine Light comes on and goes off after 2 seconds, when the ignition switch is turned to ON, replace the Ignition Control Module and coil:

https://www.askmehelpdesk.com/cars-trucks/faq-how-troubleshoot-repair-maintain-hondas-selected-other-vehicles-46563-4.html#post265896

I've never seen a fuel pump on a Honda or Acura go bad, even though many people suspect them and get them replaced. Usually suspected fuel pump-related issues are related to fuses, main relay, ECM, or ignition switch.