Steve, I did see a dermatologist when I had chronic hives for months and discussed with him my thoughts that it was linked to the surgical hardware I had in my body. He didn't think so. I have since had the hardware removed and don't have hives anymore. My allergist who is a functional medicine doctor did believe that the hives could have been related to an immune response to metals and was more open to that possibility. Hopefully your body will work through this allergic response soon. A topical lotion like Caladryl might help with itching too. I have also used Arnica gel which reduces inflammation and pain. Itching is actually the low end of the pain spectrum. It can be a reaction to the PEG (polyethylene glycol) which the Pfizer vaccine has, and the Moderna has a related ingredient that would also cause a cross reaction in a person who is allergic to PEG. Here is a link that talks about allergies and Covid vaccines.
https://www.cdc.gov/coronavirus/2019-ncov/vaccines/recommendations/specific-groups/allergies.html
I had an allergic reaction to PEG after a Pfizer vaccine for Covid. I wasn't able to get a 2nd dose and talked to my allergist who advised me to take an antihistamine like Benadryl and 3000 mg of vitamin C before getting the next vaccine. I was able to get a J & J vaccine instead, and ahead of time, I tested my reaction to Polysorbate 80 (it is in the J & J vaccine instead of PEG). They say you can have cross reactions to it if you are allergic to PEG. Polysorbate 80 is a food additive. I tested it by eating ice cream that had it and it gave me a headache, but I was able to control it with antihistamines. I had the J & J and had a headache for 2 days, but taking vitamin C and antihistamines kept in under control. Then I felt fine except for a sore arm for about a week. My allergist also chose the J & J vaccine for himself and he said it had fewer side effects than the M-RNA vaccines. J & J is made similar to a flu vaccine from a killed virus source.

I will always ask if a vaccine contains PEG. I needed a tetanus shot after a wasp sting, and it did not contain PEG and I did fine. PEG is also used in prep for colonoscopies and is what Miralax is, so it is a common ingredient to watch out for if it affects you.

Don't let me talk you out of seeing a dermatologist however. They are pretty good at catching stuff that is going to turn into skin cancer and removing it before it causes trouble. Have you seen an allergist or dermatologist before?

Identical symptoms with my skin about two weeks after my Moderna booster

I’m dealing with the same. Just under two weeks after the Moderna booster, developed dermatographic urticaria and angioedema. Prednisone taken for 5 day. Rashes persist two weeks later, with flares regularly occurring throughout each day. Physical touch and heat are common triggers; although it can come on seemingly without either stimulus. Nearly two weeks have passed from finishing Prednisone, yet symptoms persist. Good luck to you and everyone going through something similar.