Finger swollen under knuckle after mosquito bite. why would a mosquito bite make it swell. will it go down soon?

Several possibility: You may have been bitten by something other than a mosquito, may have had an unusually severe reaction to the bite, or may have developed a secondary infection due to breaking the skin while scratching. If the finger is red, warm , painful or gets worse would see a hand surgeon asap. Infections in fingers can extend upwards very quickly.