Getting HOT... water pump? sending unit?

So, I had a leaking valve cover gasket and got another one and put it on. No problem. now, very strangely, it now warms up and heads to the red. So... I put in a new thermostat figuring that may be the issue, and burped the antifreeze and it still does the same thing. It will just heat up. If I feel the hoses, they are all hot, so, I feel like the thermostat is working. I get heat out of the heater in the car and at times can turn on the heat full blast and can see the needle go down a little bit. The needle will jump every once and a while (it has done that for a long time). Now I took it out as a test after my last burping attempt and it got hot and then I turned on the heat full for a little while and it came down to the middle, I was able to turn the heat off and it looked like all was good. The next day it heated right up and never came down, it just red lined out.. (so I parked it). So... before I take the whole front end apart, to replace the water pump, any thoughts...
I just hate replacing things that are not broken, so, just checking to see if you guys think this is a water pump issue or a sending unit or reflush the antifreeze or a gauge or who knows.... 87 325ic with 99K.
Any help or thoughts are appreciated.

I have looked at a few other posts and have another comment. I can like squeeze the hoses, should I be able to do that? Or should the be hard?... with engine off, I can squeeze any of the three hoses and have it push fluid back into the reservoir. (is that what it should be like?)

did u bleed the system? and hows your fan clutch ?

Sounds to me like air in the system, or maybe a bad fan clutch. Does the temperature go up when you're driving, or only at stop lights/signs?

The upper radiator hose is the highest point in your cooling system, so any air would sit right there......and get hot......

First the fan clutch, I mean the fan goes around, I guess I don't know how to check that. Is that what I'm checking for.... blowing air into the radiator? To answer the other question, it gets hot no matter what, so, just sitting will get hot, driving will get hot.
So, if I read the responses, my best FIRST action should be to drain the system and redo the antifreeze, ... do I expect the hoses to be hard(which to me would be just totally full)??

Thanks for quick comments

when the car is running you should have pressure in the hoses. not to where they are rock solid, but they give a lil. to test the fan clutch, when the engine is warm, shut engine off, pop the hood and spin the fan with your hands. there should be enough resistance to where you need to apply decent force to move it.

another quick cheap thing is the pressure cap. they go bad all the time and tend to get overlooked