O/D off after jumping another vehicle?

So, I'm not sure if I have two problems or just one.


Car ran fine and one day my husband gave someone a jump start. I would say the jumper cables were connected to our batteries for 10min or more. Not long after I left, I noticed the O/D off light was on. So, I pressed the button thinking I accidentally turned it off. But the light didn't go away. Then it did but came back on not long after and continued to go off and on until I arrived. It didn't happen again then maybe two weeks later he jumps someone else off again the same thing. Now it's like it will randomly go off and on for a few days then stop maybe a week or longer but come back on without us jumping anyone. There is no check engine light on, but We plugged his computer up no codes, tested the battery and alternator. Battery was low voltage. We replaced battery and did the scan again this time it came back with a battery current sensor o believe it was a saved code. It's started to get worse sometimes I'll be on the highway going 70-80 and the O/D off will kick on and slow me way down to like 50 which isn't save on a busy higher.

Now I've noticed when the O/D off light is not on. Sometimes my RPMs will kind of jump back and forth or they will get up to like 5 before shifting. But every time I'm on the highway as soon as I hit 70 mph the rpms will like flicker from 3-4 and seems like because of that its having trouble shifting but I'm not sure if that's the little tug or pull I feel. Now if the O/D off light is on this doesn't happen and vice versa so I'm not sure if these are two separate issues or one issue together, please help.