Small screw in abutment fell out 3 weeks after abutment put in. It was extremely painful. Is this normal?

Typically, implants aren't painful. There can be some pressure and sensitivity when screwing into and out of the implant. Sometimes the gums can be uncomfortable for a few days after manipulating the implant. But typically, you won't have an actual pain on an implant. 

Hello Ram4957, Following suggestions can be given on the basis of whatever limited information you have shared.
1. Usually a healing abutment is placed at the time if implant placement. And it doesn't have a separate screw attached to it. The screw is inbuilt. If the healing abutment has come out and it's left out of mouth for even a day then there are chances that gums around implant collapse and decreases the opening of implant. 
This is the possible reason that it has hurt you while putting back in. 
It would be better if you could have asked your dentist to use a numbing agent. If the healing abutment is out for many days , it is advisable to enlarge the opening of gum on top of implant head so that gum doesn't get crushed in between.
2. And if your doctor has put the final abutment with a small screw. At the time of surgery. It's better if it can be covered with a screw retained temporary crown. As leaving the abutment without any Temporary crown can damage the tongue or cheeks over a period of time while eating or chewing.
3. Another possible reason that abutment has come out could be that it was not torque tightened using the wrench(hand tightening can cause loosening)  or had become loose with usage over a period of time. 
Its nothing to worry about, If the pain still persists or discomfort is there you can take a painkiller available OTC. Take care