Hey Jennifer!
I take my temp at least a couple times because I ran into that problem before and went with the one that had a consistant reading. If it was too different I'd take it a 3rd time

(is that too much? LOL!)
I don't think it matters whether you were more awake after 10 minutes or not if you hadn't gotten up or tossed n turned which would create more heat in your body.
Go with your 1st temp or perhaps one that's in the middle of the two? I've done that before too.