From direct evidence, it might be arguable whether or not "The Wedding of River Song" took place on an alternate timeline—but River Song explicitly called it that, and she presumably knows better than us, so it's a safe bet that that it was an alternate timeline.
In Doctor Who, there's a difference between alternate timelines and alternate (or parallel) universes but it would be a bit complicated to explain the difference.
So, no, it's not a parallel universe.
The alternate timeline resulted from River's attempt to save the Doctor's life by rewriting a fixed point in time (i.e., an event that had to happen). It created a frozen period of time that couldn't have lasted. Time itself was disintegrating and the universe was on course to be destroyed as a result. The end result of the Doctor negating the freezing of time was that the alternate timeline "never happened", although time travellers like River, the Doctor, Amy and Rory could still remember it.
- ↑ Actually, it would be a lot complicated.