Well technically the Doctor has just been born. They went with the theory that every time you use a teleporter you 'die', but your memories/personality/dna/etc gets copied and built into a new form in a new location. So that means that the Doctor we saw last week is completely dead, and the Doctor we had at the end of this episode and next week has just been born. (I think that theory about the way teleporters work comes from Star Trek, but I'm not completely sure. It's fun because it annoys the fanbase, because it's conceptually interesting, and because it offers a very dark view on the nature of identity and death).
There are lots of times where the Doctor used teleporters in the past as well, so we can assume that he 'died' all those times as well.
But yeah, it will probably give you more peace of mind to think of him as not actually having aged millions of years during this episode. The 'current' Doctor just has the memories of one 'trip' in that castle, he doesn't remember all the versions of him that died because technically that never happened to him. Not that version of him at least.
His memories are 2000 years old, his current body is 2000 years old (well his body is younger, but let's not go there).
Yeah, that's what I figured. I can't imagine a Time Lord being a billion years old. Even if he is a Time Lord, haha.