If you just want to get from Uppsala to Gothenburg it is very simple, visit www.sj.se and buy a ticket from Uppsala to Gothenburg. Don't faff around with separate tickets. And yes, the longer you wait the more expensive the ticket will be.
And why would you expect your friend to drive you to Stockholm to catch the train when there is a railway station in Uppsala? That would only make your trip longer and force your friend to do a 3-4 hour drive to Stockholm and back.
A single ticket will probably be a bit cheaper than two separate. But more important, it means the connection in Stockholm is guaranteed. If your first train is delayed and you miss your next train, you will be rebooked on the next available departure. If you have separate tickets, you are on your own and have to buy a new ticket at a very expensive price.