Given that this reaction is so intense and seems to happen to everyone who is contact with your cavies, we can confidently rule out any kind of allergy. I also think you are right to suspect that mites are involved – your guinea-pigs are probably suffering from Sarcoptic Mange, which is caused by a microscopic mite. If left untreated the condition of your guinea-pigs will only get worse. However, although the mites can live on humans for a few days they can’t actually lay eggs and reproduce. The life cycle of the mite is about 3 weeks from adult to egg and back to adult. The mite burrows under the skin to lay its eggs, the eggs hatch within a few days but often stay within the skin until they reach maturity in 7-14 days.

The infection is at a fairly advanced stage so I recommend that your visit your veterinarian for confirmation of this diagnosis, and for a prescribed treatment regiment that can be supervised by your vet. The normal course of action would be ivermectin injections at 2-week intervals, repeated at least twice. He will also be able to recommend treatments to address the itching, decontaminate you and your guinea-pigs’ home environment. He may also be able to prescribe steroid treatment to prevent inflammation and reduce irritation.