I take 25 mg thyroxine sodium tablet every day (tsh 9.6) will taking medicine affect repeated blood test result?

Yes!!! But you'll need to take enough of it. In other words, you should repeat your TSH in 6wks after starting your levothyroxine. In fact, check every 6wks after a dose change. Tsh should decrease as you take higher doses. But watch for side effects, too. Aim for TSH in lower half of your lab's reference range w/o suffering from palpitations, tremors, anxiety, insomnia, etc. Keep in close contact w/doc.
Taking Medicine. I would hope so. Wouldn't you? If you are on the right medication to treat your hypothyroid condition then the TSH level should improve. But, it is not uncommon to need more than the starting dose. Thus physicians will test regularly and adjust the dose until your thyroid levels are normal.