Swollen thyroid (goiter) could cause many of your symptoms. As the others have said - an ultrasound will determine whether you have a goiter, nodules or other thyroid issue.
TSH is an indicator of thyroid issues, at best, so simply having a TSH test won't diagnose a thyroid condition since there are conditions for which low TSH is "normal". You should ask for thyroid antibodies to determine if you have Hashimoto's or Graves Disease.
If it is your thyroid causing pressure on your neck, they should be able to pick that up on the ultrasound, especially if it is pressing against your carotid artery/jugular.
I had a multinodular goiter, and I could see one of those thyroid nodules that was sticking out to the side (like a finger), it would move up and down when I swallowed. That nodule was behind my carotid artery. I didn't have any pain associated with it, but all people are different. It is possible that it could be a thyroid nodules, there are also some other possibilities.
With swelling/swollen sensation under your chin, under your left arm, and down your left side and under your collar bone, I wouldn't immediately assume it is thyroid related. It is possible your body is fighting off a sinus infection caused by the allergies (not sure if you've been tested). Swollen lymph nodes under the chin are commonly caused by cold or flu or other upper respiratory infections.
Alternatively, it is possible you may have had Covid and are experiencing "long hauler" symptoms. I'm just a random person on the internet - so I'm not saying in any way that I think you might have had Covid, but I feel like I should at least point this out as a possibility since the locations of many of your symptoms are locations of lymph nodes: under your armpit, just above your clavicle/collar bone, under your chin, and all throughout your neck. I had my thyroid removed and my "central compartment" was full of swollen lymph nodes due to Hashimoto's, it felt like a huge weight was lifted off my neck when I finally got my thyroid (and a total of 14 lymph nodes out).
Just out of curiosity, are you taking any allergy medication or just acid reflux/heart burn medication? If it is caused by seasonal allergies I don't know if that would help. If it is allergies, allergy meds might help. If it is something else entirely, none of that medication will help.
I'm so sorry you have to deal with this. Those are confusing symptoms to say the least. I hope you feel better soon.
It doesn't sound like a thyroid issue. Have you had a CT scan or MRI? White blood cell count not elevated? It sounds like it is structural given the duration.