That is a very good question. From your description, it is recommended that you be evaluated by your primary care doctor
because this seems to be a very aggravating situation and it has been going on for quite some time now. Your primary care doctor will be able to best assess your medical history and current symptoms and complaints, and decide upon the appropriate medical work up. He or she may decide to refer you to a specialist. He or she may order special blood work, or skin tests to assess what is going on with your skin. Have you noticed that the itchiness and peeling are in a band like manner around the fingers that you were wearing the rings on, it is not clear from your description? If that is the case, it is likely that you have a skin allergy to the metals in your rings. If this is the case, you may have to avoid these metals so that you do not continue to have the peeling and itchiness that you are experiencing. If this is a skin allergy, you may consider benedryl cream to lessen the irritation. Aggressive hand moisturizing is another important way to lessen these symptoms.