Yes, having an Underactive Thyroid - Hypothyroidism - plays havoc with our whole body as our cells, which require active T3 to function lacks enough thyroid gland hormones and that's why we are supplemented. Once you are diagnosed as hypo, you don't pay for other prescriptions (not much of a consolation when you feel so ill).
Always get a copy of your thyroid gland blood test results with the ranges for your own records and you can also post on a question for members to comment on them.
It takes time to feel better and the GP should take a blood test about every six weeks approx with an increase in Levothyroxine until you feel so much better. Some GP's think it is o.k. to get your TSH within the normal range but that doesn't always make us feel well.
Take your levothyroxine on waking with a full glass of water before breakfast and wait about 1 hour before eating. You can always take it last thing at night, not having eaten for 2 hours before.
When your next blood test is due, also ask for a Vitamin B12, Vitamin D, iron, ferritin and folate. Also ask if he will do a Free T3 (most probably not) but it's worth asking. Usually B12 and Vit D are low.
It is slow and gradual to get to an optimum medication but you may be lucky and feel well quite soon.