Are you gluten,casein (cows milk) and soy free? A bit of a must with Hashimotos. The ibs could just be that if you're not and the weight gain. I dropped a stone in 3 weeks when I went gluten free.
HRT meds definitely interfere with thyroid meds. I've just gone through it, stopped caffeine, alcohol, spicy foods & chocolate and really bad flushes stopped.
I'm guessing Oroxine is just T4? If you are not converting T4 to T3 efficiently you will have weight gain, increased cholesterol, brain fog...
You may need to think about adding T3 or switching to NDT (natural Dessicated Thyroid) I'm sooo much better on NDT
Also healing gut. Over 70% of the immune system is in the gut. Good probiotic. bone broth, collagen powder all really good.
Turmeric, cinnamon & ginger all good for inflammation.
Do you have blood results? Good to post on here for advice.
Have you had Folate, Ferritin, B12 & Vit D tested?