Hashimoto's is the most common cause of hypothyroidism. It's very easy to test for Hashimoto's, simply by testing for thyroid anitbodies, Thyroid Peroxidase Antibodies (TPOab) and Thyroglobulin Antibodies (TgAb). If either/both of these are elevated that would be the basis for a diagnosis of Hashimoto's.
You should get your doctor to order these tests as soon as possible.
Untreated, or improperly treated, hypothyroidism can cause miscarriage so it's necessary to make sure your thyroid hormone levels (not TSH) are at optimal levels prior to getting pregnant.
That said, is TSH the only thyroid related test that was done? Your doctor should have tested Free T4 and Free T3, which are actual thyroid hormones, whereas TSH is a pituitary hormone and is an indicator, at best, of actual thyroid hormone status.
If you've had Free T4 and Free T3 tests done, please post their results, along with corresponding reference ranges so we can better assess your situation.
Autoimmune conditions tend to run in families, so if your aunt has an autoimmune, it wouldn't be unusual for others in the family to have one or more autoimmune condition either. It's important to note that not everyone in the same family would get the same autoimmune condition. For instance, I have Pernicious Anemia and Hashimoto's - my son has Type I Diabetes and my daughter has Lupus... those are all autoimmune conditions.
Do you have ANY other autoimmune conditions?
As a person who has one autoimmue issue, they are at increased risk that they will have additional autoimmue conditions. Not a gurantee, but inceased chances.
Autoimmune thyroid issues can. Hashimoto's can definitely cause infertility, especially when it isn't fully managed (TSH > 2.5). But this is treatable.