I've had both, so here's my $.02. Fibroids should be visible via ultrasound. Sometimes it's difficult to see ones that are inside the uterus without an HSG. Also, intrauterine polyps can contribute to heavy bleeding and I don't think those are usually caught without an HSG.
As for thyroid issues - the best site I've found is here
. Unfortunately hypothyroidism is way underdiagnosed and can negatively impact fertility without treatment. A typical thyroid test includes TSH, both types of antibodies (to rule out Grave's and Hashimoto's), and T4. The problem is that the range for a "normal" TSH level is somewhere from .4 to 5 and (in the case of hypothyroidism) if you're a 4.5 most docs still consider you normal. However, studies show that TSH levels for optimal fertility are between 1-2. If you're having hypothyroid symptoms and infertility, I'd encourage you to find a doc who's willing to get you toward the low end of normal. Another challenge with the test presents is that T4 needs to be converted to T3 (the form the cells can utilize). Just because T4 levels are normal doesn't mean your body's converting properly. This is why some people who take synthroid (to treat hypothyroidism), which is only a T4 supplement, still have hypothyroid symptoms even though their T4 and TSH levels are "normal". Ideally lab work will also look at T3 levels. All you ever wanted to know about your thyroid
The website link is really a wealth of information and I highly recommend it.
As for the clots, I hadn't heard about it being linked with thyroid - doesn't mean it isn't though. It makes sense to me with fibroids (although I can't say I really had that much clotting surprisingly) because fibroids can make the uterus work a little more sluggishly although there may be other reasons why it can contribute to clotting.
I had uterine massage done a few months ago (abdominal massage that focuses on optimizing the circulation to the uterus and position of the uterus) and the therapist mentioned that sometimes if the uterus is really congested it can lead to clotting, and dark colored blood. Different things can contribute to uterine congestion - constipation (if your guts are moving slow it impacts movement of everything in the abdomen/pelvis), abdominal/pelvic scars, endometriosis, the bones of the pelvis being compressed/jammed, shallow breathing (diaphragm movement contributes to healthy movement in the abdominal/pelvic organs) etc.