Transmission or fuel pump/line

I have a 1991 Honda Prelude with a recently (within 6 years) new engine. I have only had the car for about 7 months. In the last month, it would not start, and it ended up receiving a new main relay. Two weeks before, it went through the recommended 185,00 mile check up, and it passed in all areas. After getting a new relay, it was fine for about a two week period. A few days ago, it started to stall, when the accelerator was pushed, especially when the car’s speed reached about 20mph. After revving the engine a little, it would then jump up to speed. The RPM gage, when in park or resting has it set at above 1 RPM. After one day the car’s temperature gauge also immediately went all the way up to the dangerous heat zone after being started. Even with turning the heat on, it would not return to normal/ about half way. It feels as if the car skips out of gear when reaching the twenty mph mark. Is it a transmission problem or fuel pump problem? I realize no person can just read about it and diagnose the issue, just any help would be nice. Should I take it to a dealer or another mechanic, its an old car, and most of the specific parts are not being made any longer.

Your post is a little confusing so I’m not sure where to start. If the temp gauge jumped up to the hot position IMMEDIATELY after being started, you have a gauge, sending unit or wiring problem. A car can’t overheat in a few seconds, there is just too much thermal mass to deal with. No, I wouldn’t take a 91 to a dealer, as a matter of fact, I would never take any car that was out of warranty to a dealer unless it was for a very make specific problem.

I would definitely not take a car that old to the dealer. They’ll hose you. Use an independent mechanic. They’ll do a better job and when you find a good one, it is always good to have a working relationship with him, especially with an older car like this. It could be related to fuel delivery, it could be spark related, etc - but you got to start somewhere, so maybe look at fuel delivery first:
You may want to replace the fuel filter (it may have two, that particular prelude) if it hasn’t been done in years. It is usually a cheap thing to do and can be a DIY job. A mechanic will likely want to check the fuel pressure too.