Usually no — Allegra (fexofenadine) and Benadryl (diphenhydramine) are both antihistamines, and the NHS says not to take two antihistamines together unless a doctor tells you to; the main risk is added drowsiness, so check with your pharmacist first.
Both are antihistamines, but they differ in how sedating they are: fexofenadine (Allegra) is a "non-drowsy" antihistamine that mostly stays out of the brain, while diphenhydramine (Benadryl) is a "drowsy (sedating)" antihistamine that enters the brain in large amounts. Stacking two antihistamines doesn't relieve allergy symptoms much better and mainly adds side effects — chiefly excess sedation. The NHS guidance for both drugs is the same: "Do not take 2 antihistamines together unless your doctor advises you to." There is one recognized exception — for a severe itchy skin rash, a doctor may deliberately pair a non-drowsy antihistamine by day with a sedating one at night for a few days to help with sleep.
The biggest concern is additive drowsiness: combining a sedating antihistamine like diphenhydramine with anything else that makes you sleepy (including alcohol or another drowsy antihistamine such as chlorphenamine, promethazine, or hydroxyzine) can make you very tired and impair driving or operating machinery — don't drive until you know how it affects you. Use the lowest effective dose of each and never double up on products that already contain an antihistamine (read combination cold/allergy/sleep labels). Older adults should generally avoid diphenhydramine except for serious allergic reactions, and people with glaucoma, breathing problems (emphysema/chronic bronchitis), enlarged prostate or trouble urinating should be especially careful. Talk to your pharmacist or doctor before combining them, and seek medical help for a severe allergic reaction (trouble breathing, swelling of the face/throat) rather than self-treating with two pills. Do not combine these together routinely on your own unless a clinician has specifically advised it.
This is general reference, not medical advice, and not a guarantee of safety. Interactions depend on your doses, health conditions, and other medicines. Always confirm with your pharmacist or doctor before combining products, and follow the dosing on each label.