Yeah, you should be fine. I'm assuming your router does NAT (Network Address Translation), which means that your computer isn't actually on the Internet (in IP Address terms) and can't be accessed directly from there.
(There is a way of allowing access from the other Internet systems, called "port forwarding" on the router, but you'd have to turn it on and set it up. If anyone (or a website) tells you to do that, be sure you understand the reasons in full: if not, don't.)