You can try Free & Clear conditioner. However, if you're treating a contact allergy you have to eliminate all products that have it not just hair products. I have fragrance contact allergies and I react on my scalp and neck. But contact can be almost anywhere on your body and you will still react on your scalp if that's where you react. If you want to avoid fragrance (it's in almost everything and in all but 1 or 2 medicated shampoos) you'll need to avoid it in hair care, body care, makeup, household cleaners, laundry, etc. Anyone can use the SkinSafe website and app and you can choose to eliminate products with fragrance or all of the top 10 contact allergens.
I use Free & Clear conditioner only because my hair was very dry. There's a good chance that you do not need to shampoo at all or don't need to use very often. I haven't used anything but conditioner on my hair for about 2 years. Because of that, I no longer needed a leave in conditioner or products for frizz.