It is specific to your machine and your userID.

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In an unsecured network, you would have to secure you machine. They would not be able to view your history unless they were able to access your computer either physically or remotely. Make sure you have a firewall and an antivirus and do not enable your guest account. Also make sure your login account has a password.

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I have firewall and antivirus.
I only see it the view>explorer>history and if i type the first letter of the specific site in the browers itself.
Theres no history of it the temporay internet files or the google drop down window.

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You need to clear you browser history. In IE 7, it is in internet tools -> Delete -> Delete History.

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There is the potential of someone sniffing your packets on the network though. Then at that point all they have to do is run a capture and then they can decipher everything you are doing on the internet. Websites, email, chat etc. I recently came across a program called hotspot sheild that creates a VPN tunnel to secure all communications to and from their network. If you are paranoid about someone snooping from a remote machine I would use that. Other than that you are ok.