First, welcome to Flyertalk and to Women Travelers. You'll find a wealth of information here.
To answer your question, no you can't carry-on pepper spray, but the TSA does allow you to check up to 4 oz of mace or pepper spray provided the container has a safety device to keep it from accidentally discharging. (Check out the permitted and prohibited items list at tsa.gov). It's best to check with your carrier though too as some have more restrictive policies and don't allow pepper spray even in checked luggage (you'll usually find this info on their websites).
As for women's safety tips. There are quite a few threads on this subject that you'll find using the search feature that you'll find at the top of the page (type in security and search the Women Travelers forum). Here are some particularly good ones.
Travel Safety Tips
Single traveler security tips