My Synthroid (thyroxine) level was too high and I became a bit hyperthyroid. I am nursing, should I be concerned about extra hormone passing to my baby?

Should be ok. Levothyroxine is excreted into human milk in small amounts. Levothyroxine, in replacement doses, is not expected to cause adverse effects in the nursing infant. Your doctor will adjust your dose to bring it into the normal range.
During pregnancy... Estrogen levels increase thyroid binding globulin, making the need for increased production of thyroid hormones. If you are on thyroid replacement, then your thyroid needs will increase during pregnancy. If total T4 is measured, it will be high. You need measurements of free t3 (liothyronine) and maybe free T4 with a TSH to determine thyroid status. Hypothyroid women can have major fetal problems.
Should be no problem. If your breast milk contained extra thyroid hormone, the baby's thyroid would simply cut back on how much it made to keep baby's thyroid hormone levels in range. PS - women usually need a boost in thyroid hormone dose during pregnancy, and a return to lower pre-pregnancy doses soon after delivery.