What were your actual T3 and T4 test results and reference ranges when you started taking the desiccated bovine thyroid? How much were you taking daily? Did you self diagnose, or was it done by a doctor? What symptoms did you have at the time? What were your Test results and reference ranges after stopping the med?
It is hard to determine without reference ranges, but I am suspicious that there was no reason to start you on thyroid med other than the doctor's concern about the TSH. However, a high TSH is frequently associated with Hashi's which you said you did not have. Were you tested for both TPO ab and TG ab? If you are in the U.S. then I expect that the Free T4 and Free T3 results are well within range and also not a reason for concern. The hair loss could well be due to other issues like low iron. The weight gain could be associated with many things. The tiredness could be due to low B12, among other things.
Your current test results appear to confirm that you did not need to take thyroid med. Seems to me you should go back to square one and start over without thyroid med. It would be a good idea to test for Vitamin D, B12 and ferritin (a storage form of iron).
Back to your question about how long for the med to normalize. T3 will dissipate in about 4-5 days. T4 will drop about 50 % the first week and 50% every additional week. So the T4 effect will be essentially gone in about 4 weeks.
Vitamin D should be at least 50 ng/mL, B12 in the upper part of its range, and ferritin should be at least 100.