Hi Ona/axsai. Your depression may be associated with your hypothyroidism and NOT require Elavil, Zoloft, or any other antidepressants. In fact, many of these drugs interact with thyroid medications and, sometimes, change the effectiveness of the thyroid meds. However, it's always best to discuss this with your doctor before stopping or changing your medication regimen.
Several studies have shown great success in treating depression in thyroid patients currently taking T4-only meds (Synthroid, Levoxyl, etc.) by giving the patient some T3 (Cytomel) as an additional supplement. In some cases, the T3 was given in combination with the antidepressants to speed their effectiveness, but other patients have reported decreased depression once their thyroid levels were balanced and did not need antidepressants at all. Perhaps you need a medication adjustment, particularly since you say your hypothyroidism is not yet properly managed.
You mentioned previously that you have many hypothyroid symptoms, despite taking 0.2mg of Levoxyl twice a day, and that you've tried many of the thyroid meds with little help. It really sounds like you're undertreated (or not absorbing/metabolizing the meds properly), and I think your depression is just another sign of this. The addition of some T3 may help, but remember it is a slow and gradual process to become balanced.
Personally, my long-term depression has much improved since my thyroid meds were corrected. But I have Hashimoto's thyroiditis and tend to fluctuate with my symptoms, so I also use an herb called Maca to balance this and my other symptoms.
You need to find a doctor who will investigate why your body is so resistant to your thyroid hormone. In the time leading up to your July Endo appointment, try to keep a notebook that tracks your symptoms, medications, responses to meds/foods/environment, your diet, etc. I think it may be helpful to have a thorough log of what's going on in your life so you can discuss it with your doctor to investigate what may be impacting your health.