When you follow someone, they'll get a notice on their dash (similar to FB's news feed) that says "username started following you". It won't have your email address.
Unless it's a password protected blog (which it isn't, because you can see stuff on it) it doesn't even matter if you have a Tumblr or not, you can read it.
And yes, Tumblr is mostly pictures. If her theme has a search box, you might be able to search tags such as "personal", which is commonly used for that reason.
Having said all this, if she finds out you may have broken a lot of trust with her, and I don't know if that's worth it.