I am shocked that you have a TSH of 5.08 which, if we are on adequate medication should be around 1 or lower.
Ditch your GP if he always told you you are in the normal range. Do you have the ranges for your blood tests. The reason for requesting these is that labs throughout the country differ and it makes it easier to comment. You don't say what dose of levo you are taking, but it's too small whatever the amount.
You have to make an appointment and have a good talk with your doctor, by telling him you are underdosed with levothyroxine. NO wonder you are feeling rough. Email firstname.lastname@example.org and ask for a copy of the Pulse online article. She will send one after the holidays. In it look at question 6 and discuss an immediate increase (ask him to prescribe 10mcg of T3 initially to add to your T4). He may be reluctant but point out that Dr Toft says he can. After six weeks have another blood test and ask for a print-out from the receptionist (for your own records) so that you can post for comments.
Don't take levo on the morning of your blood test, take it afterwards. Always take levo when you waken with 1 glass of water and wait around 1 hour before breakfast. This helps with the uptake of levo. If you take other medication/supplements leave 4 hours between levo and those.
If your GP hasn't tested your Vitamin B12, Vit D, iron, ferritin and folate ask for these to be done as we are usually deficient.
We have to read and learn so that we can recover our health. Weight gain is a clinical symptoms of undiagnosed or undermedicated hypothyroidism.
Make appointment with your GP for the New Year.