Google The 5 Day Extended Patch Test, which is given by a specially licensed dermatologist or allergist. I had the True Test Kit and one other panel kit. This test checks for contact allergies like the chemicals and elements in rubber, metals, fragrance, preservatives and as many as 100 other contacts. Although I did have hand eczema for 10 years beginning in middle age I didn't know about testing to find the cause. After 10 years my entire body, not just nose area, began itching, tingling with stinging with the pins and needles symptom you describe. There was no physical rash and I had a hard time getting my derm or family practice doctor to understand as I looked just fine. I learned about Allergic Contact Dermatitis, ACD and a test for it, the 5 Day Extended Patch Test. My derm wasn't licensed to perform it so was referred to another doctor, an allergist. Of the 78 test site I reacted to 5 and now avoid because I control my contacts. I had to change 98% of my wardrobe, bedding, grooming products, 3 of the 5 classes of steroids and all my shoes plus more. Yet now I lead a productive and am free from ACD symptoms. Even if you learn you don't have ACD, you will have eliminated another reason for your itching.
So, check out this test for ACD and also research Perioral Eczema and Roseaca, both cause itching around the nose, yet I believe both are associated with a rash. Yet, my internal skin symptoms for ACD didn't have external symptoms so that's why doctors were confused.
Right now try to only use simple facial products which are free of many common allergens, buy Grandma's bar soap for face and body on Amazon, this year became a Mayo SkinSafe products. Safe for ACD sufferers. Only 2 ingredients, Google this soap and how it is made so not to be concerned 1 of the 2 ingredients is lye (it becomes glycerin in the soap making process). Stop using facial tissue with softeners. Only use 100% cotton linens washed with a safe detergent like Charlie's Washing Powder and the new All Free and Clear, fragrance free is safe for many.Do not use any form of memory foam in mattress or pillow; polyurethane foam is ok. Memory foam is made from elements is rubber as common allergy which I have. Vaseline original is about the safest moisturizer on the face, except with Perioral eczema. With Perioral steroids feed this form and occlusive moisturizers, like Vaseline trap bacteria. When I had this form I needed to wash face daily, apply a topical px antibacterial and an immune suppressant (non-steroidal called elidel) and it cleared up the rash and itch in a few weeks and hasn't returned. I am curious if they tried the elidel px on you? Yes expensive, $300 a tube, but with my insurance $100 and will last for years. I should have not used my insurance and used the free px plan GoodRx to buy the elidel. On the internet you get a coupon at GoodRx good at all your local pharmacies (put in zip and it will list all, even if they are in grocery stores). I learned with GoodRx I could have gotten the elidel for $89 at Wal-Mart. Elidel is not a steroid, it is an immune suppressant and worked wonders for me clearing up rash and tingling itch around the nose and mouth. It's much safer.
My internal skin symptoms had doctors baffled and before I learned about patch testing had a complete neurological work up thinking it might be systemic, like lioness mentioned a rheumatologist. My neurologist did not think it would be nerve issues because normally if one has nerve damage (I had head injuries in the past causing mild concussion and neck issues) the tingling, pins and needles and such are usually felt on just one side of the body; my issues were random and all over, head to toe, both side. Of course sleep was impossible and without learning the cause I would have finally committed suicide as I had not slept in months. Living with pain 24/7 becomes unbearable. Lack of sleep is a form of torture. I would lay there and think of easy and pain free and non messy ways to end it all. After all the tests for nerve damage only learned I had carpel tunnel and believe me my ache in my wrists was not even a concern of mine compared to the internal skin pain.
Keep a list of all the diseases you have been checked out negative for, all the tests you have had, all the meds you have tried and then look in new directions just like you are doing now. Best of luck.