1996 Chevy S-10 fuel pump

I replaced the stock fuel pump because it went out. Since then, I've had a starting problem. When I turn the key to ACC I can hear the pump come on but it sounds like it's running under a load. I can crank the engine over but it will never start. I turn the key off and then turn it back to ACC making the pump come on. It sounds like it's running under a load for a second but then sounds like it clicks and then runs with a high pitch like normal. The engine easily starts after it clicks and becomes high pitched.
Is there some sort of pressure switch or actuator switch that needs to be replaced to fix it or might there be a leak that bleeds off the pressure and lets the fuel drain out?