What do doctors do when their patients have a medication allergy to the medication they want to prescribe?

Find an alternative: This can make treatment difficult, but luckily there are usually alternative treatments available. Also there are some medication allergies that a board certified allergist can do a desensitization for that can allow for the medication to be taken without reaction. Also., some medications "allergies" are really only adverse effects that may be tolerated if needed. Get evaluated by an allergist.