Hello and welcome to JustAnswer,
It indeed sounds like you have low thyroid, or, what we call HYPOTHYROIDISM.
The test you had, however, is not the best test for this. Something called the TSH, thyroid stimulating hormone, is typically the best test. It should be HIGH if you have low thyroid.... trust me.... it should be HIGH if you have this.
It sounds like someone has already diagnosed you if you are on levothyroxine as it is the medicine for low thyroid.
Click on the link above to learn all about it, but you do describe the symptoms and need a complete check of your thyroid done by your physician. Also, many times, in looking a the thyroid, it is necessary to get an ultrasound of the thyroid to rule out nodules or masses which occasionally can represent cancer.
Get back with your doctor ASAP and take the reference above with you.