I will be brutally honest here. If you have broken down in front of the CEO, chances are that you have now created an image or perception in the mind of that CEO about yourself.
And let me tell from more than 12 years of experience, it's very difficult to change people's perception. Especially people who are at very senior position. Reason is that these senior folks only work is to judge people and retain best folks and remove laggards. They can't afford to make mistakes in having wrong people around them.
Chances are you may not get better projects or work. Or you may be able to change his perspective after working your ass off and showing him how best your are.
I know you wanted sympathetic answer but unfortunately I had to address the elephant in the room. These hard conversations is what will make you tough. End of the day don't take anything personally.
Work is just work. If you don't like a particular organization, just move on. Because the business will not think twice before laying you off for their reasons.