Syncing/Updating problem!

I do not have any access to the computer I have originally used to sync. Now I am wanting to update my phone and have to use my new computer and it is telling me that I will lose all my purchases from itunes if I do so on this computer!? I have already transferred all my downloads to this computer, but am not sure if it is ok to update now, or will I still lose all these purchases?! How can I update my phone?