Just put 35 inch tires on my 2000 silverado and now my converter wont stay locked in at 55

I would think so. P stands for passenger and LT stands for light truck. The store that sold the tires should be able to get the correct recommended pressure.
You went down from 17 inch to 14 inch rims ??

may have put tires on the opposite side they came from

The stock size rim is a 16" just as info.. Try a 265/70/15. It will give the width and the heigth that is taken away by the one inch missing on the rims.

Yes , tire sizes can be changed without any problem , as long as you don't go too different. Here is how a tire is measured........
195 is the width of the tire 19.5 centimeters , 55 is a measurement of the amount of rubber outside the metal rim , in your case it is 55% of the width ( 195 ) the r15 is the rim size 15 inch.
You could go to a slightly wider tire with a lower profile , like a 205/50/15 or a slightly narower tire with more profile like a 185/60/15.
The important thing is to try to stay close to the same overall hight . if your old tires are 25" in diameter , try to stay close to that , or you will throw your speedometer out of true.

could be a plug cat but you fuel pressure is low for this vehicle, it should be 55-62 psi, I would check the fuel filter on the frame and see if it is pluged, this can also take out the fuel pump, make sure the pump is not growling it should sound smooth, these trucks are known for pumps!

changing to a deeper profile will alter the rolling circumferance of the wheel thereby altering your speedo reading,you could try 215/35/17 they will fit but at a very serious cost.......

35 psi

Check your tire balance. When you have an out of balance tire or a belt in the tire has shifted you will experience a shacking only at a certain speed.

I assume you have checked the transmission fluid. Try changing the fuel filter. You wouldn't believe how often people confuse transmission problems with fuel filter problems. The engine is starving for fuel, and therefore, power, and the transmission does everything it can to try and find it.

Either replace the O2 sensors, or put a black piece of electrical tape over the check engine light.