Try Ice. If you ice the fingers with the mosquito bites, they will be less itchy. This has been the most helpful "at home" treatment for itchy mosquito bites.
See your doctor. Diminished production of protein by the liver may lead to swelling. Other causes should be ruled out.
Depends on cause. If the only problems is swelling: rest, I've compression and elevation are standard remedies. If due to other causes such as a tight ring (remove it) or lymphatic obstruction or trauma, etc, the root cause should be determined and treated first.
Find the cause. You first have to figure out why it is swollen. Given you age it is probably a sprain. These can be swollen for many months. I would keep you finger moving so it does not get stiff. See a hand surgeon and get an xray to make sure there is no fracture.
Swollen fingers. CAN BE DUE TO trauma, infection, arthritis, inflammation, nerve issues, tumor, or excess retained fluid due to systemic problems. IN general ice and elevation and gentle motion help but if there is prolonged swelling, pain, redness, change in sensation, loss of circulation see someone soon. There are so many things I can list, that even if just swelling and chronic get evaluated.