When you had your second blood test, did you follow this procedure which I think you may not have done as you are newly diagnosed. This procedure allows the TSH to remain at its highest as food and time of day affect the result and the doctor might adjust dose unnecessarily due to the TSH only.
The blood test should be the very earliest possible and don't eat before it but you can drink water. Also leave approx 24 hours between your last dose of levo and the test (the day before put your meds somewhere else so you don't make a mistake) and take hormones afterwards.
Also levo should be taken first thing with one glass of water and don't eat for around an hour. Food can interfere with the uptake of levo. If you prefer you can take levo at bedtime, as long as you've left about 2.5 to 3 hours after eating.
If GP hasn't tested B12, Vit D, iron, ferritin and folate ask for these the next time a test is due. We can be deficient which can also give symptoms.
If people gain weight it is usually very slow to happen. Some people don't gain weight.
Re your clinical symptoms, i.e. pain, fatigue etc are clinical symptoms and your doctor should have raised your 50mcg dose to 75mcg and every six weeks you should have an increase until your symptoms resolve and you feel much better. The aim should be a TSH of 1 or lower not somewhere in range.
Always get a print-out of your results with the ranges for your own records and you can post if you have any queries. It is a learning curve if we want to recover so we have to read and ask questions.