Thank you for the query.
Possible bacterial infection would cause wound area infection at first. Moreover with bacterial infection you should have fever
Itchy rash can be caused by an allergy
or local skin infection
and does not have to be caused by wound contact with chicken meat. It seems to be just a coincidence.
However it is very hard to give accurate answer not seeing your rash. That is why I suggest you to visit dermatologist
first. Some local anti-inflammatory agents might be necessary.
Hope this will help.