After seeing the thyroid Q I am going to say that I personally (this is just my opinion for myself) would not start the Zoloft at this moment. You have out it off for a long time, and I would say addressing your thyroid is more important and taking thyroid drugs will be screwy for a while, and if you take both drugs at once you won’t know what’s going on.
Also, I want to emphasize that I really really want you to test your thyroid again within 4 weeks of starting your thyroid meds. Don’t wait 6–8 weeks if that is what they are recommending. At 4 weeks you will not get a proper reading of the final level your thyroid will be at the drug dose your taking, but what it will do is if you are already moving into a hyper state you will catch it before it is really bad. It takes weeks to adjust thyroid, so every time you are under medicated or over medicated you probably have been like that for a few weeks, and then it takes a few weeks to get to normal. What this means is most thyroid patients spend 2–3 months not in normal range when their medication dose isn’t right. A quarter of the year! This is why frequent testing initially is important, and in the future if you seem to be very stable in a dose you still should go once every 6 months for a blood test.
Also, regarding only waiting 3–4 weeks for your first blood test after starting thyroid meds, really pay attention to how you feel. If you feel much better get a blood test, so you know the numbers you feel best at and can shoot for that as your normal. It might take you many months to get in tune with your symptoms related to your thyroid. Many endocrinologist like TSH between 1 and 2. Below 2 I’m not good. Can’t sleep well, heart is pounding, heart rate up to 80 at times just sitting in the couch. My hair is falling out, my eyes are dry. I’m very symptomatic. My ideal is 2–3.5. Above that my blood pressure gets high. That’s me, everyone is different. That’s why you need to know you, and your doctor most likely will not be good at figuring it out or knowing or charting when you felt best. Your doctor might be good about letting you test more frequently, and care about your subjective assessment of how good you feel, which is great, but you need to get familiar with your numbers. At minimum your TSH.