Allergy as such is not my forte, but you symptoms are certainly consistent with a contact hypersensitivity. This is unusual with fruit or vegetables, but it can occur due to proteins called Prolifins in the skin.
My advice would be to take antihistamine tablets such as Piriton which you can get over the counter.
Sketchy answer, I know, but it is the best that I can do.
In the summer a friend of mine was diagnosed as being intolerant (not allergic) to tomatoes after over a year of intermittent itching and rashes. From then she stopped eating tomatoes or anything with tomato products in them (difficult when tomatoes are one of her favourite foods) after 4 and a half months with no tomato products she is now back to her usual self, no itching, no rashes.
Her doctor has recommended she tries this for 9 months to a year before re-introduce them. It’s hoped that giving her body time to ‘forget’ its reaction she will eventually be able to eat tomatoes again. If you think it is a food intolerance try eliminating one food at a time for about a month and monitor any adverse affects/improvements you should soon be able to tell if there is any progress if not its unlikely to be that food so try something else. Does your GP practice have more than one GP? Try asking if there is one who has an interest in food intolerances there is usually one in a practice with a number of GP’s.
Good answers so far. It could be pesticide / herbicide residues have you tried organic. Looks like a long trial and error experiment to isolate the cause but worth doing