The word gotten just sounds wrong to me sometimes, yet it always comes out of me naturally. I noticed it earlier when I was writing an email to someone; I typed out that I had gotten something, then quickly backspaced and put in the more majestic received instead. Then I realized, I don't actually know if gotten is good grammar or not. It sounds like slang and somehow seems wrong when I see it on my screen, but it still has its place in the English language. In fact, I've quite recently learned all about it.
Gotten is a past tense form of the verb to get. Get just means have, hold, receive. It can also be used to mean to experience ("I got sick"). The past tense form of get is got; the past participle of got is gotten. A past participle is a word that's used with had, have or has.
Therefore, it's perfectly acceptable to use gotten if it's being used with its companion word. I have gotten sick before. ...Unless, of course, you're in Britain.
They stopped using gotten when Queen Victoria was still ruling England, and that was a long time ago (pre-Civil War). But people in the States never did stop using it, so it's still proper English if you're on that side of the world.
That said, I still don't like the word. Gotten can just about always be replaced with prettier words like obtained or acquired, which look much lovelier on the page. In dialogue, however, gotten may sound more natural to your inner reading voice. If gotten seems to make the text flow just the right way, type it on in there -- because yes, it's proper English and when used the right way it's perfectly good grammar.