I am sorry you are not feeling as well as you used to. I have looked at your profile but you haven't given any info, i.e. when diagnosed, medication, dose although I see from above you have an underactive thyroid i.e. hypothyroidism.
To get well we have to read and learn as much as possible about our condition, in order to get better. By now you will probably have sussed out the doctors appear not to be the best people who understand about the function of the thyroid gland, nor some Endocrinologists, more's the pity.
If you have had a recent blood test for your thyroid hormones, get a print-out from the surgery with the ranges and post on a new question for comments. If you've not had a recent one, please make an appoint as early as possible, and don't take levo before it, take it afterwards. Do you take levo first thing with 1 glass of water and not eaten for around an hour, so that the uptake of levothyroxine isn't affected. Also ask for a Vitamin B12, Vit D, iron, ferritin and folate as we are usually deficient and these need to be at an optimum too - not just 'in range'.
Re your running (I am not an athlete). Our body and thyroid receptor cells need an optimum dose of thyroid hormones (levothyroxine, natural dessicated thyroid hormones or T4/T3 (levo plus liothyronine - the two main hormones) to work normally and efficiently. Sometimes levothyroxine doesn't work as well for some people into converting to sufficient T3 (the active hormone). Levo (T4) is inactive.
No matter what your GP says, (they don't know) when we exercise it depletes our T3 which in turn causes symptoms, I assume like you have above. If we are not underactive our body replaces what we have used up but if hypo, because we are 'low' anyway and adding hormones which our body cannot replace normally so we have to have an optimum thyroid hormone for us to function as we want to. That's easier said than done as levothyroxine as been promoted as the only replacement for hypothyroidism. Those of us on this site have found that we don't necessarily get well on levo but some have found the benefit of an addition of some T3. Others have moved onto T3 alone or natural dessicated thyroid hormones (these used to be the ones we all got before the blood tests were introduced along with levothyroxine) (a synthetic hormone).
I note you say you have no other symptoms on levothyroxine and am glad that that's the case.