It sounds like some variation of inflammation in the elbow. That can be due to:
- Repetitive stress involved in handball or other non-sport related activities
- General inflammation in combination with the stress
- Injury due to hyper-extension or impact
Fortunately, for inflammation based injuries the solutions are fairly similar for acute (one-off) injuries:
- Ice the joint to at least numb the area
- Compress the joint and move it through it's full range of motion--don't forget internal and external rotation as you do this. NOTE: start with small movements and increase range of motion as pain allows.
- Remove the compression
- Rest the joint
To deal with chronic (re-)injuries you'll have to adjust some other things:
- Use light strength training with high reps to get blood to flush out the inflammation
- Modify your exercise to routinely incorporate "pre-hab" (corrective action before inflammation sets in)
- Modify your technique if the technique is to blame
Light strength training to rehabilitate your elbow would include both elbow flexion (some form of curl) and extension (press or cable triceps extensions). Use a light weight that won't aggravate the joint, and that you can use for 3 or 4 sets of 10-15 reps. After doing this 3x a week for a couple weeks or so, you should notice the joint feeling better. Give more emphasis to the action that you use less. Also, do not lock the elbows during extension related exercise because your goal is to flush blood through the joint.
IMPORTANT: If your injury is due to a known injury during the sport, do get it checked out to make sure there isn't any non-inflammation related damage. If there is traumatic injury in addition to inflammation, the protocol I outlined will make things worse until the trauma has been remedied.