I don't know the answer to your question, however, I wanted to add that taking zinc in excess can deplete your copper reserves. How much are you taking? Why are you taking zinc- was your zinc level low? I know low zinc levels can affect the conversion of T4 to T3, which would raise your TSH. No idea about high zinc levels though. It doesn't seem as though taking normal doses of zinc for 4 days would have that much effect on your zinc level or thyroid.
Doing a quick internet search led me to the conclusion that high levels of zinc can lead to anemia, which can exacerbate hypothyroidism. Again, after 4 days, that shouldn't be the case.
TSH fluctuates quite a bit and it could be coincidence that you are testing on days that your TSH is higher.
You should test first thing in the morning because TSH is higher then. Also, I would really insist on getting your results. I don't know how it works in the UK but in America, a patient is entitled to their medical information.
Is your Dr also testing your free T4 and Free T3?
If you can afford it, I would go to a private holistic doctor who is well versed in thyroid care. I thank my lucky stars that I don't have to deal with the NHS.
Patients of the NHS in England and Northern Ireland have rights to their health records just as we in the US do. For specifics, search for 'NHS patients' rights'. I would never be the patient of any doctor who tried to refuse access to my own lab reports.
TSH fluctuates daily, in circadian rhythm. The differences you see may be related to nothing more than that.
__________________ "We can complain because rose bushes have thorns, or rejoice because thorn bushes have roses." Abraham Lincoln
That's very unfortunate because those TSH are indicative of hypothyroidism, not even borderline. If it helps the AACE (American Association of Clinical Endocrinoligists) recommends a lab range of 0.3-3 for TSH and the NACB (National Academy of Clinical Biochemistry) recommends a TSH lab range of 0.4-2.5. A TSH greater than 2 is suspicious for hypothyroidism. My hypothyroidism caused infertility and I have never had a TSH greater than 3.3- it's been as low as 1.25! I would insist on having Free T3 and Free T4 checked as well. Since you are in the UK, you probably won't have much luck with NHS doctors and need to go private. What city are you in? I can send you some info on top recommended doctors for thyroid care.