My 1YO baby was bit by a mosquito it seems and she have developed a terrible rash. Is there a home remedy to bring down the swelling, I don't want to give her allopathic medicines?

Try a basil rub -- my late grandmother used this method on my brothers and I when we were young. She'd finely cut fresh basil leaves and rub it on the spot that itches. Alternatively, you can boil some water with basil leaves. After the water has cooled and the basil has steeped into the water, take a clean wash cloth and dip it into the basil water. Dab the wet cloth where it itches and it works wonders!