Looks like you are having conversion issues. This is a random website talking to this from a functional medicine perspective:
Conversion of T4 to T3 Thyroid Hormone - Root Functional Medicine
Look also into some of the normal deficiencies for hashimotos patients. Vitamin D, B12, Iron (all four tests and Ferritin).
If you are stressed try some meditation. I like Tara Brach. Tons of free videos on Youtube and her website. She's a bit Buddha like, but I swear those meditations helped me get through the worst situations I had...anxiety, PTSD, etc. There are other meditations out there as well that can lower stress. Deep breathing techniques help also. And for me, just taking a lot of warm baths really helps.
Once your thyroid levels improve, you may not need to do these anymore...though they are always a good idea.
I had this going on at first also. High FT4 and low FT3. One thing that actually made a big difference for me was switching to name brand Synthroid instead of generic Levothyroxine. They are not equivalent. In fact, 100 was too much Levo for me, but I'm on 112 Synthroid now. So that could take some time to settle if you did decide to switch. However, best to try one thing at a time. Keep this in mind if things don't improve. Tirosint is another popular one (probably more popular than Synthroid). Both are quite a bit more expensive. Use coupons on their website to help. Still will be much more expensive than generic.
Keep this in mind also. It can take a long time for things to settle after any dose change. Some say it takes a month, but I personally think it takes 3 months+ for things to settle. Not fun, but you can try adjusting diet and addressing nutrition and see how that goes. It can make a pretty dramatic difference for some folks.