I am T2, but also have an autoimmune disorder that causes delayed anaphylactoid allergic responses. Not as serious as anaphylaxis, but unpleasant and debilitating. All sorts of blood allergy tests came back as negative, despite me having skin rashes and itchy hives regularly. They are absolute misery and you have my sympathy.
I only got a diagnosis of my disorder following a referral to an allergy consultant after I had an allergic reaction to general anaesthetic. All the usual skin tests showed no allergy to the usual allergens, but a specialist blood test for tryptase levels revealed the blood disorder. I now have to take daily anti-histamine in varying doses depending on symptoms, but I do get relief from the rashes. Also have steroids when necessary.
I would recommend you ask for a referral to allergy consultant. There are very few in NHS but if you are having swelling of the face and lips this could cause problems. Be persistent with GP in asking for referral. The standard allergy tests do not always reveal the cause of the allergic type symptoms.
Hope you find a solution soon.