How long will hives last if i'm having an allergic reaction to medication?

Depends on half life: Different medications have different half lives. A half life is the time is takes for 1/2 of the drug to be metabolized and passed out of the body. It usually takes 3 half lives for a drug to be considered out of the body. If you know the half life of the drug, then you can make an educated guess about how long the hives will last. It also depends on your body's own metabolic rate (fast/slow).

Less than one week: Typically, hives due to a medication will last for only a few days; two weeks tops. Medications that stay in the body for a few days could cause longer reactions. Adverse reactions to medications should always been discussed with and shown to the prescribing physician, so that the true cause is identified, and your chart is marked so you aren't given that medication again in the future.