98 cavalier bypassing relays

I have recently started having problems with my heater blower fan for my a/c and my radiator fan not turning on. I pulled out my relays and replaced them with the compatible ones from autozone, yet both still are not working. i then got some wires to jump the outlets to bypass the relays both now work. Here are pics to see what i did: here is an overview of both here is the radiator fan outlet here is the outlet for my blower fan this is only a temp fix for the problem, but until i can fix it, can i run it fused and not worry about it frying my a/c or radiator fan? any and all help is appriciated. Any ideas also why all my relays, even new ones wouldnt work?

working for now. i stuck a wire into the plug that pin 86 on my relay plugs into and connected it to the body and everything works. yay