I'm sorry to hear that you experienced a rash after taking a dose of Bayer aspirin.
Good news, you can safely take Benadryl (diphenhydramine) with Bayer aspirin ('Bayer ' is a brand name and 'Bayer aspirin' products simply contain aspirin). There is no known interaction between the two.
Benadryl, an antihistamine, is a fine option in this situation as it can certainly help lessen the severity of your symptoms (hives and itching) but it is important to remember that it can be quite sedating.
If you need to avoid being sedated, a non-drowsy antihistamines, like Claritin or Allegra, are also options for you.
I am curious if this is the first time you have experienced such a reaction with aspirin. Aspirin sensitivity is a fairly common problem, and reactions can range from serious (e.g. swelling and respiratory problems) to fairly mild (e.g. hives, itching).
If you were recommended to take aspirin by your doctor, be sure to let them know what you experienced. They may be able to pinpoint what kind of sensitivity you have (if any).
In some cases, they may be able to 'sensitize' you to aspirin by giving you very low doses and working your way up if it is medically beneficial for you to be taking it on a consistent basis.
Some studies also show that 'pre-treating' with an antihistamine before giving a dose of aspirin can help to reduce the risk of adverse reactions.
I just want you to know that even though you experienced a reaction this time, that doesn't necessarily rule out the use of aspirin in the future!
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There is no known drug interaction between Benadryl (diphenhydramine) and aspirin.