We were all ignorant when we first came here. You have to educate yourself; you're moving in the right direction.
Your doctor has to provide you a copy of all lab results on request. They can charge you for the copies, but most don't if it's just a few.
TSH is a pituitary hormone. It's nothing but a messenger from the pituitary to the thyroid to tell it to make more thyroid hormone. So, it's a very indirect measure of thyroid status. FREE T3 and FREE T4 measure the actual thyroid hormones and are a much more direct and stable measure. Most doctors were taught in med school that TSH is the gold standard in thyroid testing. It isn't. Some even order FT3 and FT4, but they basically ignore them.
The guideline for FT4 is the middle of the range. This is based on where many of us had to be before symptoms were resolved. The target for FT3 is the upper half of the range, and for some, it has to be in the upper third. (BTW, reference ranges vary lab to lab, so they have to come from your own lab report.) Another mistake doctors make is assuming that everyone will be symptom-free no matter where in the ranges they fall. I may have to be low in the ranges, you may have to be high. The whole range should be used to find where you feel best.
So, I'd say that the first thing you should probably do is get those lab reports. You have to determine if she's just ordering TSH. If she's also ordering FT3 and/or FT4, we need to take a look at those to see where in the ranges they are. If she's not, you can request them, but finding a new doctor is probably a better option. It would be great if you could get those reports on which she based your meds changes. A brief history (since the adjustments started) with lab results and meds changes would be very helpful. How much does she usually adjust your meds by in one step?
Do you know the cause of your hypothyroidism, i.e. have you been tested for Hashimoto's thyroiditis antibodies?
How long have you been on thyroid meds altogether?
I will ask but she didn't volunteer the info. I feel so ignorant. But I will educate myself. I don't even know where those levels are supposed to be. thanks.
Is your doctor testing FREE T3 and FREE T4 as well as TSH? If so, please post those with reference ranges. The "rollercoaster effect" usually is a result of dosing based on TSH and ignoring FT3 and FT4, which are much more direct measures of thyroid status.