Why is it hard to reverse? Feels like I'm reversing with the hand brakes up. on 1993 Toyota Corolla

My mileage is 300k plus. I have to press the gas hard for the car to actually move in reverse and when i release the gas pedal the car jerks like the wheels are locked up. This only happens after driving for some time, not when engine is cold.
Engine - 5A-FE 1.5 (I'm actually from Trinidad, not the US.)

Asked by for the 1993 Toyota Corolla
Ever checked the actual differential fluid/lube which is seperate from the transmission??
No. I didnt know it is separate from the transmission. What's the best fluid to use?
80 w 90 diff lube... hope it's not completrly out!!... And might not be the problem at all... i have seen this before though!
I'll still try it. thanks
The check plug is difficult to see... and get to... but is there!! Most people including some that work on vehicles are not aware it even exist... thus the problem with low/no lube!!! ... l've been doing this for a very long time... and own a 1993 Corolla so this isn't just some rookie guess as for the differential lube being seperate from the trans!!..
Well there's no separate diff with my model, according to the mech shop I went to today. They knew about the separate diff fluid with the AE100 but mine doesn't have it they say. He told me it may be a sensor prob. Something leaking probably burned a wire somewhere. I'm going to an auto electrical shop tomorrow. What do you think?
Oh, and the car is now revving and going nowhere. I have to switch off, then restart and it works for about a minute before it goes into revving mode. So frustrating...
Your 93 Corolla is one of a kind!!
1 more answer
Has the trans ever been rebuilt? If not, that's probably what it needs? Or it could be a simple fluid and trans filter change? Try that first.