Are IP addresses unique and trusty?

Recently, I got a notification in my gmail account saying that my account has been accessed from a completely different place (in the United States, while I belong to, India, and there are zero chances of any of my friends or any sort of relations being there, even!) place as said by the IP address given there. (It gave me the recent IP address from which the account has been accessed and there it was, an IP ID belonging to this place in the US). How can this have happened? Is there any chance of changing our IP address (I saw a weblink sayin "change your IP address") from the one that's been provided? If not, what's the chance of such happenings?