Are at home tsh testing kits good to go if i'm already on thyroxine n just need lab updates?

Depends: Are the kits FDA approved? Without such review and approval it is probably not a good idea to rely on the results. Have a healthy diet, exercise 30 minutes/day, drink plenty of water daily so your urine is mostly colorless, have safe sex, no tobacco alcohol weed or street drugs. For nutrition: http://www.choosemyplate.gov/. Get HPV and Covid vaccines. Wish you good health!

Testing: Will be most accurate while under the care of an endocrinologist and/or your primary care physician as to timing and consistency in type of test used. They may be able to recommend such a test, but consistency will be needed in the long run.