I think Mum is right, unfortunately - whilst it is slightly possible that it is one product, such as the primer, which you may be reacting to, and that it might be a different ingredient in it that is causing the problem, but if you are allergic to acrylic then you will be allergic to all three systems - gel, l&p and wraps, and also to the adhesive that sticks the tips on etc.
In this case, then you won't actually be able to use any system I'm afraid. Sorry! But a good tech should be able to help you make the best of your natural nails. Regular manicures, good care, nail treatments etc should get you a lovely set of nails just as nice as any extensions you've had. Personally if you've had that much pain and suffering, I don't think it would be worth putting yourself through it again. Find a good tech who will take the time to listen to your situation and find a natural treatment program that will work for you. A good tech shouldn't listen to what you've suffered and just take your money anyway. To be honest it's daylight robbery and downright irresponsible (I'll get off my soapbox now!)
Sorry I can't give you the answer you might have been looking for, I just wouldn't put yourself through more pain, hun. I'm sure there'll be some Geeks in bedfordshire who can make your nails look lovely without having to have extensions.
Good luck, please let us know how you get on!
Lol xx