A service would probably help it some. Yeah it's 46re.
Now would be a good time, if you can weld, to add a drain plug to the pan.
Service goes as follows:
Drop pan, change filter (3 screws, t25 torx if i remember right), adjust bands per service manual. Now, transmission builders have recommended to me going 1 full turn extra when doing the backing off portion if the trans is new, since yours is having a couple issues follow the factory service manual. Should be 72in/lbs and 1-7/8 back off for the front i think? Double check that. Rear should be similar but luckily you can download the factory service manual on this forum (it's great).
When reinstalling the pan, do NOT use any rtv. Good way to kill a trans. The rubber gaskets are preferred vs the cork. Use a tq wrench on the bolts, don't want to strip any threads, 13ft/lbs is all it is. Fill via the dipstick tube, it's gonna take awhile and you'll need a skinny funnel. Add about 5qts and start the truck then shift it through the gears slowly about 4 or 5 times to kinda warm it up and then leave it in neutral and running when you check. This will give you accurate fluid level.