Thank you for your query at DoctorSpring.com.
I understand your concern.
TSH of 4.88 isn't way off-target or abnormal. However, due to your symptoms, you have been started on a low dose of thyroxine.
Your dose of 50 mcg is fine, as long as it is helping you.
You need to control on diet and exercise regularly to lose weight as thyroid does not seem to explain your weight gain.
You need to repeat TSH after 6-8 weeks of starting Thyroxine. If the TSH is in the range of 0.4-2.5, then continue the same dose. If not, the dose has to be adjusted based on the value. Repeat TSH will suggest if your dose is right.
Regarding conjugated estrogens and Thyroid, women on thyroid replacement therapy may require higher doses of thyroid hormone while receiving estrogens. There is no effect on thyroid as such.
I hope this was helpful. Let me know if you have any queries.