Water Pump

Hey guys. I have a 1985 ford Thunderbird, I have just recently changed my radiator because I was having issues as far as pressure in my radiator. Radiator was badly clogged. I was getting tiny bubbles in which looked like soap in my resevour tank, and bubbling out through the cap. Now im getting bigger bubbles like I have air in the system. I changed my radiator and my thermostat. Seemed to fix the problem. But today I noticed my temp gauge was acting crazy going from cool to hot and back down. Didnt stay hot just went up for a split second and dropeed back down and stayed at cool for the rest of my trip to work. Thought my thermostat may be sticking because its new. Well when I got home let my engine cool for about 2-3 hours. I went out popped the radiator cap. In which still a little back pressure, like it was still hot. Filled up Radiator, left cap off started car, and noticed that water wasnt circulating through. And also when I revved it up kinda high in park, the top radiator hose sucked shut. I Was wandering if the water pump isnt working properly will the water back up in radiator and cause pressure causing the thermstat to read hot? And will it cause air bubbles in my water system? I have been told my head gaskets may be leaking pressure into the water system. So can u help me? I dont have the cash to keep sticking in the car.