Hi Suzanne, I'm lurking from 3T but I have Hashimotos and Graves, so I might be able to answer some of your questions.
Hashimoto's is an Autoimmune disease that makes your body think your Thyroid is a foreign body and attacks it. Because your Thyroid is being attacked it will increase the amount of hormone it realeases to try and fight off the attack. Eventually the Hashimotos will cause hypothyroidism. You will need to have your levels checked, and as you become hypothyroid you will need to be on Synthroid and increase your dose over time. Now how this can effect infertility; if you have an AI related Thyroid disease, like Hashimotos, even if your thyroid levels are good there is a chance that the antibodies can be found in your ovaries and cause a lower AMH or weak ovulation (which is my issue, but my AMH is fine), but this isn't an issue for everybody. Also autoimmunie disease aren't always active, so you flare up. Meaning you might go through times when your antibodies and TSH are higher, but they can settle themselves and be calm for a period of time. I agree w/ the RE you should seek the help from an Endo. My RE doesn't do anything w/ my Thyroid (or lack ther of) as long as my Endo keeps her in the loop. I get my Thyroid levels tested monthly.
Feel free to PM me if you have any questions.
::backing out of IF::