If I got you right, you want that you can login to your accounts on "public services" (Facebook, Youtube, etc are public in a sense) only from your current computer, and not from your brothers or friends computer.
If you want to limit possibility of login to some site from computers in your home, that's possible, either using some kind of parental control or firewall. Actually it is easier to disable access altogether than to disable login, but everything is possible in your home, if you have enough time & knowledge.
If you want to limit login to some public service from other computers in the world - it's impossible. Or better, other people can try to login to your accont(s), but first they need to pass either one-step or two-step authorization (which some services recently enabled) to be logged in.
You can do that (enable two-step authorization on services which have that option), if you fear for the security of your account(s).