I am sure that you already know that your iPad can only be sync'd to one library at a time and this means only one computer at a time. Your iTunes account really has nothing to do with this as it is the mechanism by which Apple knows who to bill for what. However, several devices can share the same library and the same account. I believe your issue stems from the fact that you are using two different computers.
Obviously Apple knows what you have purchased, but unfortunately, there does not seem to be a way to look up your purchasing history like you can with
Amazon for instance. You can look up your downloadable software history and hardware purchase history, but not "content" like apps, music or movies.