If the shaky thing happened once and in the rain it was probably a misfire cause by some ignition stuff or something similar getting wet (plug wires, coil, crank sensor). If the other stuff gets sorted out then you should have someone sort that out. Its not good.
No one can tell you whether or not the car is worth major transmission work. That all depends on the condition of the rest of the car.
I occasionally check the fluids, transmission and engine oil: both are ok///
If you didn’t check the transmission fluid TODAY (or the oil for that matter), then you have no idea if it is ok or not. So the question isn’t “do you occasionally check the fluids?” - its did you check the fluid since this happened?
The bottom line is that if you are in gear and the engine is revving up when you step on the gas, but the car isn’t going, then your transmission is slipping really badly. If you were to end up really low on fluid it could do this. If you don’t cook the thing while its slipping like this (which wouldn’t take long) then sometimes you can get the leak fixed, fill it up and drive on. But if its slipping and the fluid is actually fine, then chances are you just need a new transmission.