The answer is yes... as long as the neighbor knows what she is doing.
First of all, deleting your browser history has nothing to do with anything (this just deletes information from your computer). The problem is that your neighbor can intercept your communication with the internet.
If you are using my Wi-Fi, every packet that you send anywhere goes through my router. It is not very hard for me to intercept these packets and do whatever I want with them. And I can even change the information in the packets coming back (i.e. changing what you see on the websites). The URLs you are visiting are in the packets, as well as any of your unencrypted data going either direction.
If the website you are visiting has good security (i.e. https done correctly) then it is hard for me to see the data that is being sent in either direction, but I still can see the websites you are visiting. There have been many cases of security holes in websites that made a mistake allowing an attacker to see data even on encrypted sites.
So in short... for your neighbor to see what websites you are visiting is pretty easy. For your neighbor to see whatever data you are sending to or receiving from an unencrypted site is also pretty easy. Seeing encrypted data is difficult on a well designed website (but they can still see where you are going).