Welcome to the forum. You are asking good questions. I'm not taking any hormone replacement medications. I'm still trying to get euthyroid with Methimazole. Therefore, I'm not personally familiar with Levoxyl. Maybe some of the members will join us soon and leave you more information.
As for breast feeding, the one thing I can think of that could pass to your baby is Levoxyl. In drugs.com
it says that it can pass into breast milk, but it is not expected to be harmful to the baby. I recommend asking your Dr. and Pediatrician about this, especially since your baby has had thyroid problems in the past.
I think you should report your new symptoms and let your Dr. tell you if she would like to move labs to an earlier date.
Wish you the best with your labs and your new dose. Please keep us posted.
The best to you and your baby,