Nice that your GP acknowledged that your symptoms were real, most do not.
No need to be worried about the ultrasound scan which is non-invasive. A gel will be smeared over your throat and neck and a hand held monitor will record the size and condition of your thyroid gland and the size of any nodules which is what the lump is likely to be. 95% of thyroid nodules are benign but any over 1.5cm with suspicious features or nodules over 2cm are investigated further.
Thyroid is probably swollen because TSH 32 has been flogging it to produce more hormone.
In the early days Hashimoto's can cause transient hyperthyroidism which is what happened in Feb for you to have TSH 0.1. The lymphocyte infiltration will have destroyed thyroid cells which dumped hormone in to the blood causing the hyperthyroidism. Destruction of cells atrophies the thyroid gland which is then unable to produce sufficient hormone.
There is no cure for Hashimoto's which causes 90% of hypothyroidism. Levothyroxine treatment is for the low thyroid levels it causes. Many people have found that 100% gluten-free diet is helpful in reducing Hashi flares, symptoms and eventually antibodies.
For maximum absorption Levothyroxine should be taken with water 1 hour before, or 2 hours after, food and drink, 2 hours away from other medication and supplements, and 4 hours away from calcium, iron, vitamin D supplements, magnesium and oestrogen.
It takes 7-10 days for Levothyroxine to be absorbed before it starts working and it will take up to six weeks to feel the full impact of the dose. Symptoms may lag behind good biochemistry by several months.
You should have a follow up thyroid test 6-8 weeks after starting Levothyroxine. Arrange an early morning and fasting (water only) blood draw when TSH is highest, and take Levothyroxine after your blood draw.