for you - hope you feel better soon!
It took a few months for me to feel better once I started on Synthroid and it was very gradual, like you suspected. My doctor started me on the lowest possible dose - I think it was 25 mcg - and checked my TSH after six weeks. Then she adjusted the dose and repeated the TSH in six weeks, etc. etc. until we finally hit on the right dose. I think the whole process took about six months due to the six week wait between blood tests.
I was lucky and didn't have a lot of symptoms before I was diagnosed so I didn't notice a dramatic change, even after my Synthroid dose was stabilized. But getting my TSH in the right range did allow me to lose the weight, which was what I wanted!
Good luck! You're on the right path and hopefully you'll be feeling a little better every day.