What can cause a 1 year old child to develop alergies and rashes on its skin from mosquito bites?does any skin cream help?

Mosquito bites: That's what mosquito's do - cause those huge local reactions, and in a rare person, even more widespread reactions. If i get a mosquito bite on my leg, it will often swell to the size of a small cup saucer. It's due to histamine release locally. Sometimes cool compresses to the area are helpful, but for such a large reaction, topical anti-itch meds probably won't do much. Could try oral benadryl, (diphenhydramine) .

Mild allergy to bite: It is not uncommon for children to have mild allergic reaction to insect bites. Topical hydrocortizone 1% cream is easy to find and can be used a couple of times per day on the bites to alleviate itching, swelling and redness. Occasionally an oral antihistamine such as Benadryl (diphenhydramine) can be used if the child is very bothered by it. If pain, fever, or worsening rash, call your doctor.