I have read that Mohammed would have came in a period after the first messiah and before the second messiah. Does this mean that Jesus is considered as a messiah or who else is considered to be that? And why isn't Mohammed himself a messiah?
Maybe the confusion comes from the word Messiah.
No, even according to Islam, Mohammed is not the Messiah, Jesus is. Islam belief is that Jesus is alive in Heaven and will be back at end times.
The reason Mohammed (or any other prophet) cannot be the Messiah is simply because he died, and god forbids a dead person from coming back. (I can look up the reference for this if you insist, but on the other hand, the references on the global subject are very numerous)
Jesus should not be confused with Al-Mahdi, who is yet another figure. There is only one Messiah: Jesus.