I started my truck and heard a high pitched tone coming from the rear of my truck, kinda near my rear fuel cap. Then I switched fuel from my rear tank to the front tank. I shut it off and just put it in the on position and it turned on, but kept running.

Is it a new fuel pump I need?

 

Hmm, a high-pitched whine that's loud enough to hear over the rest of the stuff is often (but not always) the sign of a fuel pump that's on it's way out. It might run for a week, or another six months. No way to tell.
But the pump running constantly is different. This usually indicates that the computer just had it's unfortunately all too common capacitor meltdown inside. Easy to fix if you're technical about such things, or it can be replaced entirely.

But I would try at least one other test if you did not already. Switch to the other (supposedly good) pump and turn the key back on. If it also runs continually, that's a pretty good sign that at least one, if not all three of your capacitors has reached the end of it's life.
And of course the best thing to do is to wait for someone more knowledgeable to pop in and confirm all that!

If the second pump does not run all the time, then it's likely not the computer. But I can't imagine a single pump running on when the other works fine. I think the power comes through a single relay and is controlled by the computer alone.
If the '95 has two fuel pump relays though, then try swapping them one for the other to see if the problem follows the relay.

That's all I've got. Good luck and I hope it's as simple as a bum fuel pump.

Paul

 

Classic symptom of a failing/failed computer (PCM). Remove the PCM, from the engine side of the firewall, then open it up to inspect for signs of leaking capacitors or burned components/traces.