Yes, she can. But, sending away for duplicates is something you do. You have to wait until you are 18, otherwise you would need the signature of your parent or legal guardian. Sending away for it does not take very long though and you can even pay to get it on an expedited basis. The form is available online. The cost is pretty low. Here is the link: http://www.doh.state.fl.us/planning_eval/vital_statistics/birth_death.htm
Social Security also has a form. http://www.ssa.gov/online/ss-5.pdf. You fill in the form and take it to a local social security office. I suggest you get the birth certificate first and then get the social security card.
You may want to have items mailed to you at an alternate location such as a friend's address or get your own P.O. Box.
Please note that this answer is not intended to establish an attorney client relationship and is limited to the facts presented.
Once you turn 18, you are able to request copies of all items for the issuing agencies.
Ana Maria D'EScoubet, Esq.
1801 SW 3rd Avenue
Miami, Florida 33129
This is not legal advice and no attorney client relationship is created by this communication.