Hi, is there a medicine for allergies in eating chicken and eggs? I get skin rashes which are very itchy everytime I eat. Thank you.

Avoidance. The way to avoid allergic reactions is to avoid eating chicken and eggs. An antihistamine such as Allegra or Claritin (loratadine) might blunt the reaction somewhat, if you take it before eating the offending food, but it won't work as well as not eating the food in the first place.
Avoidance. Currently the best treatment for food allergies is identification of the food and complete avoidance. Taking medications in an effort to eat the food is not a good idea. An allergist can confirm chicken/egg allergy.