I will be accessing a computer in a different state via Teamviewer. The sites I work on have very high security measures in place. Is there any way possible that my actual IP address can be revealed in addition to that of the computer I'll be dialing into?
The IP you connect from will be available to the computer you access. The sites you access in a web browser from that computer will only see a connection from that computer, and will not be able to determine the IP you used to connect from on Teamviewer. If you run any applications outside the web browser, it would be possible for them to detect the incoming connection, but only if they are specifically looking for it.