You can try heating up a spoon and apply the heated spoon to the mosquito bite or apply a cold compress or ice pack to the mosquito bite will should help get rid of the mosquito bite sooner.
Also applying some calamine lotion to the mosquito bite can help stop the itching and make it go away sooner as well.
Another home remedy for treating a mosquito bite and relieve the itching of the mosquito bite is to take some baking soda and water and make a paste.
Then apply the baking soda baste to the mosquito bite which will help it stop itching.
Either way avoid scratching the mosquito bite since it can make it worse and lead to infection.
The mosquito bite should go away within one to 2 weeks but may go away sooner if you treat it using the above home remedies for getting rid of the mosquito bite.