1) If you suspect the fuel pump, a mechanic can connect a meter where the fuel line comes into the engine to test the fuel pressure. If there is good fuel pressure, then the fuel pump most likely isn't the problem.
2) Most importantly, I would check to see if you have a vaccum leak somewhere. A vaccum leak is certainly a possibility on an older vehicle because all of the rubber vaccum lines get rotten and cracked and they need replacing after a certain number of years just as routine maintainence. This would certainly cause terrible issues when you go up a hill or are at highway speeds and try to accelerate.
3) Dirty fuel injectors certainly could be the problem, but if they are that dirty and clogged, a fuel additive might not be strong enough to clean the injectors properly. A good mechanic will have the tools to do a proper fuel system cleaning where he will clean the injectors, fuel line that goes to the injectors and clean the throttle-body, etc.
4) A very dirty air cleaner could be the culprit. How long has it been since the air cleaner has been changed? Typically, when you get an oil change done, the air cleaner is checked too because this is an easy additional $30 or so that the service center can add when the air cleaner is dirty and they always want to check the air cleaner and change it.
5) There could also be something like a Crank Position Sensor being out of whack, and this would cause bad timing issues that might only show up when you are putting the engine under load. But, I would check all of the easy and less expensive culprits first before worrying about a Crank Sensor.
I will try to make this as simple as possible, I am most certainly not a mechanic. I have an 86 Dodge, bought new and taken good care of. Today, while driving up a steep hill, and having had to stop, I could barely get my car to accelerate. I had my foot right down on the gas (it's an automatic) and it would barely move. By putting it in first and then second I was able to finally get my speed up to 60kmh. There was no shuddering, shaking or noise, it just didn't want to move. I have no problems starting it or driving it on flat roads, no stalling either. I put in a new fuel pump 3 years ago so hopefully it's not that. I've also put in fuel injector cleaner but don't think it's had time to work yet. The mechanic I called said he doubted it was the fuel pump but my brother in law says it might be. I was going to take it in for an oil change tomorrow, plus air filter, but now I don't know if that will help the problem or not. I've been reading everything I can find on the net but haven't found anything relating to my problem. In all cases there have been complaints of hard starting, stalling, shuddering, noises etc. of which I have none. I would really appreciate any and all advice before I go spending money I don't have. My main concern is the fuel pump which costs a fortune, could it be as simple as an oil filter? or changing the air filter? Thanks so much.