Swelling of the left side of my face after the dentist rescrewed a dental implant screw which had come of. What to do?

Gum tissue grows fast and that's why after re-tightening of that screw, swelling up to 3 days is common. so take medicine and wait for 3 days. if any issue after that visit your dentist.

If the titanium implant has become lose after 2months then it's unlikely that it will fuse with the bone again just like that with replacement. Just take an X-ray and share if possible if your face still has swelling. There can be a risk of reinfection. Start doing warm saline gargles and go for a check up in the vicinity. 

The screw that goes into the implant only touches the implant. There is no way replacing a screw into an implant would cause an infection. It's more likely that when the screw was tightened, it pushed the gums a bit and put some pressure on them. That can cause some inflammation and takes a few days to subside as your gums react to that pressure.