The condition you have is called hypothyroidism and it's a very common condition. Since you're on a very small dosage of medication and have only been on it for a week, it's unlikely that you'll feel much relief from symptoms yet, as it takes 4-6 weeks for the med to reach full potential in your blood.
What symptoms do you have, other than the 10 lbs of weight gain?
Do you have a copy of the actual blood test report? Was the T4 test a Free T4 or was it a Total T4? They aren't the same tests and don't provide the same information. If you have a copy of the report, please provide the reference range, since ranges vary lab to lab and have to come from your own report.
When are you supposed to go back to have your levels retested? Typically, levels are retested after 6 weeks, and dosage is adjusted as needed to alleviate symptoms, according to blood work.
You should also ask your doctor to test thyroid antibodies to determine if you have Hashimoto's. The tests you need are Thyroid Peroxidase Antibodies (TPOab) and Thyroglobulin Antibodies (TgAb). You need them both, as they are both markers for Hashimoto's and without both tests, you could be misdiagnosed.
You may need other tests, as well.