There are some parts of this I like. The first part about moms with back pain is good. The details about sciatica, middle back pain, etc. are too much info.
You might also want to paint a picture because what you do is so easy to describe. Start with something like “You know how when you’re pregnant everything hurts? Well I get rid of those aches and pains for pregnant women.”
One last thing- lose the hard pitch (if you know… tell her...). it comes across as pushy salesperson and you want to come across as helpful healer.

Thank you for your comments, Laura. 

So, as a corrected Elevator Pitch…
Hi.  I am Dr. Anna Madland with Atlee Chiropractic Center.  I work with pregnant moms to relieve pain during pregnancy.  You know how when you are pregnant and your hip is aching and it feels like your leg is going to give out? Well, I get rid of those pains for pregnant mom’s. 

Dr. Anna Madland with Atlee Chiropractic Center.  We got your back!