My car overheats, even on trips as short as 15 minutes. If I rev the engine to force water into the system, it cools the engine for a few seconds, but not enough, and it always goes right back to being dangerously close to over heating, or over heating. I have attempted to run the heater in the car, on full blast as well during the entire drive, and even that does not pull enough heat from the engine.

Possible solutions that I have already tried are:

Replaced water pump
Used the gold liquid stuff to seal any possible leaks in the radiator
Replaced the tubing that connected from top of water pump to something on the engine, not sure what, but there was a hole in that tubing.
Put water directly into the radiator, problem continued while pouring water directly into the radiator.

I'm trying to avoid a mechanic, because I can't afford it, so if anyone has any further suggestions on what to try, or need further information provided, please let me know.

Try replacing thermostat, sounds like it might be stuck & not opening far enough.

You have to bleed the cooling system of air after having a leak or replacing parts...did you do that?

Trapped air will make them act like that.