Check charging system light comes on and stays on. battery light is also lit up. Just started today doing it only at accleration then it stayed on constatnt tonight

The light means that your battery is not being charged properly. It could be that when the transmission was replaced, they alternator belt was not put in properly or tight enough. I'd do the following:
1. Check battery connections to make sure they are clean and tight.
2. Check the drive belt to the alternator. It should be tight and not slipping.
3. If neither of the above is the problem, fully charge the battery with a battery charger so you can drive it for a while. Don't drive it without charging or you may get stranded. Don't let the battery run all the way down either or it may ruin it.
3. Check alternator output by driving to a nearby auto store or the place you had it repaired. They usually can check your charging system for free. The alternator could have decided to malfunction, although it's pretty new.
Good luck...

What do you mean won't stay charged ? Battery dies while driving , dies over night ? Is the battery symbol lit on the dash , check charging system message on driver info center ? If it drains over night there is a parasitic draw on the electrical system ! If while driving the battery goes dead it's not charging , with a new alternator the problem is in the electrical circuitry . Blown fusible link or fuse . This charging system is controlled by the PCM - engine computer , the heavier gage wire on the back of the alternator should have battery voltage , if not blown fusible link near the battery . The connector with three wires ,one should have B+ voltage , the other two come from the PCM .

have a load test done on the battery as there may be a dead cell Have an auto electrician check the reason for the indicator light staying on

Hi have you checked the brake fluid level ?

If you had the proper voltage regulator
control the light would be out

Need to have that checked out before
you ruin the new battery or alternator

usually caused by failed generator. Fix the generator and other lights will also extinguish. The car should jump start, but will not stay running without a charged battery. Recommend removing the generator and take to parts store for testing. Would you like instructions for removing generator?

The issue may be the alternator is going out.If an Autozone or Advanced auto is in your area usually they will test these for you at no charge. Would have the system tested multiple times because it may pass once then fail the next. If it repeatedly still passes. There may be an wiring problem at the pigtail plug of the alternator.

Its probably the alternator. It will need to be tested on the vehicle with the engine running and the light illuminated. Measure the battery voltage with the engine running. It should be at least 13.5 volts. If it is lower have the alternator tested at a shop with a charging system tester.

recheck your body ground may have surface rust on bolt, body, or connection

something staying on or your battery has had its days