The NICE guidelines suggest testing for total IgA as well as IgA tTG. Might be worth referring this your GP to this if it hasn't been done.
https://www.nice.org.uk/guidance/ng20/chapter/Recommendations#serological-testing-for-coeliac-disease
Other tests that might be worth considering for home testing include IgA anti-DGP, IgG anti-DGP, and IgG tTG. It is also possible to have a genetic test to see whether you are susceptible to coeliac disease by seeing what type of HLA gene you have. Almost everybody with coeliac disease has either HLA-DQ2, HLA-DQ8, or HLA-DQ2.2, and anyone not having one of those halotypes is unlikely to have coeliac disease.
Home tests are fairly accurate although not as accurate as an accredited laboratory. I found several UK suppliers - I have not used them, have no connection and am not recommending them, I am just giving this as an example of what is available.
Combined IgA and IgG anti-tTG:
https://www.personaldiagnostics.co.uk/coeliacscreen.html
Combined IgA and IgG anti-DGP:
https://homehealth-uk.com/all-products/prima-home-coeliac-celiac-disease-wheat-gluten-intolerance-test/
IgG anti-tTG laboratory test:
https://www.cerascreen.co.uk/products/gluten-intolerance-test?variant=38260235591
Not that I recall. I felt lousy prior to a gluten free diet and then gradually improved over 9 months. Going back on gluten for testing was very unpleasant indeed.