I have sinking carnivore shrimp pellets which I use for crayfish and axolotls, do you think theres any chance of the eels eating them?
Absolutely none at all.
Whilst growing your own guppy feeders will work quite well, your problem becomes weaning the eels onto alternatives. Provided there are live foods in the tank, they'll ignore the frozen foods. Truly, bloodworms are the best thing, but you might also try tubifex worms (annelids, not insects, so unlikely to cause your "allergy" problem). Otherwise, simply find a way to use bloodworms without touching them. Prawns are good up to a point, but they are nutritonally unbalanced and contain large amounts of thiaminase which breaks down vitamin B1.
Finally, and I can't stress this enough, if you suspect you have an allergy of some kind, please consult a medic. There are a number of serious diseases that it is *potentially* possible to catch from aquaria. Salmonella is one, and while relatively harmless (stomach upset type symptoms) to healthy people, for very young children or very old adults, as well as others with health problems, Salmonella can cause serious sickness. Fish TB is another disease, though usually (but not quite always) associated with marine aquaria. In humans this causes a temporary skin rash. Again, not normally serious, but for certain people with compromised immune systems, potentially harmful. Please do not try and diagnose "allergies" yourself just in case the underlying problem is something more serious.
It is INCREDIBLY unlikely you have an allergy to bloodworms because they are not known to be allergenic animals (unless you eat the bloodworms!). Most allergenic animals have fur or feathers because these are the things that trigger the immune response. But it is possible that your aquarium is contaminated with something else you are reacting to, perhaps a medication you used.
Cheers, Neale