I have had the same problem where my little 40l Primus 12v fridge (That I stupidly didn't tie down) got bounced on its side and luckily the cigarette lighter type plug pulled from the battery pack.
I just left it sitting upright for a couple of hours so that it and the beer could settle down then plugged it in again.
That was a couple of years ago and I haven't had a problem with the fridge since So it obviously didn't do it too much harm.
Hopefully your fridge will recover as well.

