I have no "eggs" but I take birth control pills so I have my period

Unfortunately it takes "eggs" to get pregnant. Most women with TS have ovarian failure and have to take hormonal supplements just to undergo the changes that are assocaited with puberty.

The only way for a woman to have a child when she has TS is to either a) adopt; or b) have an egg donation. So, in the end, no you will not be able to have a child.