Allergy Testing

Is it appropriate for providers to bill for specific IgE invitro (code 86003) and percutaneous allergy skin tests code range 95004-95071) before or after the following:
Removal of tonsils and adenoids 42820
Removal of adenoids 42830
Creation of eardrum opening 69436

Can either one of the listed procedures include both types of skin test and be billed all during the same encounter.

Are there any age restrictions for 86003?