Hello Keri,
Congratulations on coming out to your mother - it was hard wasn't it?
I'm not surprised that she said to you "no you can't have one of those sex change thingies" - most parents still immediately think transsexual = sexual deviant who will not be able to hold a job in society other than walking the streets, and saying no is the instinctive response in attempting to protect their child from making what they think is a bad decision.
Please don't let her put you off from sorting yourself out - you need to be able to live at peace with yourself, and simply burying things makes it much worse in the long run. My first confrontation with my mother was at age 14 - she asked me if I was trans then, and I said "No" out of fear. It's been over 20 years since that incident, life's entanglements have really gotten complex and I can now only attempt to moderate things rather than doing what I should have done years ago.