Neon overcharging problems

My charging/Battery system lamp came on a few days ago and there after that
I noticed a strong acid smell coming from the engine compartment. I figured
it was coming from the battery and sure enough the area around the top caps
were wet. I applied a meter to the battery and at first with the engine
running it appeared to charging at 12.5 volts. After a few more seconds it
went slowly up to top out at about 16 volts (The meter reads no higher) This
is my work car (My Jeep get about 14-15 mpg) and I really have to keep
repair costs down so what possible could I do to further troubleshoot and
reapir my Neon.
P.S. Engine Trouble codes at present 35,46 & 42
Thanks In Advance

 

And what year was that engine compartment (and the rest of the car) built?

You've got more than just charging problems, or you've misread the codes:

35: Cooling fan relay circuit open or shorted
46: Charging system voltage too high or too low <--Duh
42: Auto Shutdown relay circuit open or shorted, OR fuel pump relay
control circuit fault, OR fuel gauge sender unit resistance/voltage does
not change over distance, OR Z1 circuit voltage missing when auto shutdown
circuit energized.

If you had a genuine 35 or 42 situation, the engine would be overheating
and/or the car wouldn't be running.

Are you sure you checked the codes correctly? Could the "3" in your "35"
actually be a 1 and a 2 = 12, which means "Start of codes"? Go check
again.

In the meantime, the voltage regulator has failed on your car.
Unfortunately, it is integral to the engine control computer (SBEC). SBECs
very seldom fail, but when they do, this is at the top of the list of
failures. The factory fix is to replace the SBEC, and that's certainly
easy to do, but it is not inexpensive. If you are willing to put in a bit
more effort, you can install an external voltage regulator with perfectly
satisfactory results. This is only worth attempting, though, if you are
comfortable working with underhood wiring.

So, go recheck those codes, tell us about your wiring abilities, and then
we'll go from there.

DS