It is possible to suddenly form an allergy.
If your GP isn't able to help, you may need to see an allergist. They can do skin and scratch tests to find out what you're allergic to. If it's not the dogs, it could be something that is in your neighborhood that dogs might get into. For example, a common weed or grass that grows, so even if you were at someone else's house you could still get the effect of the allergy.