It sounds like your transmission cooler lines are leaking from what you described. If you are low on fluid, that could definitely cause issues. It depends on how bad they are leaking. Automatic transmissions are very sensitive to fluid level and type.
If it were me, I would fix the leaking lines and do a fluid change. Don't do a flush the transmission as it could cause more issues. Make sure you use the correct fluid and not some generic fluid. Good luck!