Allergists typically do not recommend moving to a new location to escape your allergy triggers.
Individuals with allergic rhinitis (allergies) may develop new allergic triggers after moving to a new location. I would recommend discussing your symptoms with a board-certified allergist who can discuss treatment options before considering a move. If you consider moving, spend some time in the new location but understand allergy symptoms can develop after living there for some time.
More information can be found here and here.