I am hypothyroid and I still pop the drugs the days it is the worst as long as my numbers are nornal, most importantly my blood pressure, which goes up when I am undermedicated for my thyroid.
I am not a doctor, so don’t take that as advice, but I would ask a physicial or pharmacist before you rule them out altogether. There are different types of antihistamines and decongestants. I know Cloricidin decongestant is for people with high blood pressure, I have no idea if it is considered ok for thyroid disease. I am have never taken it, but I have family members who do, on of which does have hashimotos, but also high blood pressure that she treats with medication.
I also recommend going to your smallest bathroom, closing the door and running the shower hot so it fills the room with steam, sit for a few minutes, and then take your daily shower while still in the steam (obviously turn the water down to a comfortable temp).