According to Adam Clarke's commentary, the third year of Cyrus was the same as the first year of Darius the Mede from chap. 9.
Excerpt on vs. 2:
"I - was mourning three full weeks - The weeks are most probably dated from the time of the termination of the last vision. Calmet proves this by several reasons." Source: here
It was the shock of learning of the end of the Jewish polity and the end of the hope of any restoration of Israel to its earlier glory under Solomon that caused Daniel's grief. Daniel had been asking about the 70 years of the prophesy for the return to Jerusalem and release from the Babylonian captivity (Dan. 9:2).
He had wanted to know the end of the desolation / waste of Jerusalem, and God sent Gabriel to answer that specific question. Daniel had thought he asking about the return to Jerusalem from Babylon. But, the end that was the true question, the end of the desolation was not what he expected to hear.
To be told that his people (the Jews) and his holy city (Jerusalem) would be destroyed, that the end of the desolation was the complete destruction of the very city of God to which Daniel was seeking to return made him sick at heart.
Daniel was mourning what he had learned in the previous vision in chap. 9. In chap. 10 Gabriel tells him that he was busy dealing with the king of Persia (Cyrus), and had to wait until Michael could help before he could return and explain more to Daniel. Gabriel gave strength to Daniel to hear the rest of the prophesy.
Gabriel then rehearses in chap. 11 the secular history that would unfold from the fourth king of Persia (Xerxes) through the remaining three kingdoms of the visions from chap. 2 and 7: Mede-Persia, Greece, and the Romans. That history rehearsed the wars of these troublesome times all the way through about 400 years and the rule of the king of Judea at the time of the Messiah's appearance. That king was Herod. See the history outlined here.
Daniel was still reeling from this vision, as in Chap. 12 he asked Gabriel when would be the end of these things (Dan. 12:6). Daniel was still wondering when will the desolation of Jerusalem end. He still did not quite understand that it wasn't going to be rebuilt, and asked the question a second time in verse 8.
It never occurred to Daniel that Jerusalem would be utterly destroyed, and that his question of the end of the desolation of Jerusalem was not the return from Babylon. Learning that his people would eventually be scattered and his city destroyed was completely unexpected and overwhelming.