Unfortunately, once allergic, always allergic. The best suggestion is Fiberglass or Silk wraps or a Dip System. Possibly also a UV Gel Polish system.
If it is any consolation, many technicians suffer from this reaction also.
Here is the how come and reasoning.
The technician(s) over the years continually got the acrylic liquid (monomer) on the soft tissue surrounding the nail itself. This prolonged exposure of chemicals to the skin essentially creates an effect where your body says "no more please" and tells you by the red, peeling, puffy and itching.
Acrylic - a combination of liquid monomer and polymer powder - is not really too much different than gels in its base composition. Gels, in a real simple explanation, are nothing more than partially cured acrylic. The sticky residue left after curing of the gels can also be part of the reaction equation. When the technician cleans the sticky residue from the nails after curing, if she is wiping that all over your skin also, this will cause a faster allergic reaction because there is a sufficient amount of chemicals in the sticky residue of "uncured" gel".
Any type of wrap or dip system should do well on you at this point. If your natural nails are "awful" UV Gel Polish may not do well though because it does not have the strength of a traditional gel or acrylic application. After some period (maybe 6-12 months) of a wrap system, if you are not experiencing any further reaction, your technician can try one or 2 nails back with the acrylic or gel to see how you do.
The wraps are "resin" (glue) systems, and therefor have no acrylic base which is why this is the best suggestion for a switch for you. Wraps are very lightweight and natural looking as your gels are. They do tend to be a little more brittle over time, so a little more care of how you use your nails are expected for great results!