Keep your chin up and don't get discouraged Bro - you will find a job if you keep trying. Taking criticism and learning from it is a good thing, your apology was a sign of maturity. It isn't making mistakes that's bad, it's not learning anything from them.
There is probably a machine trades organization in the area - do a search for it. Find a machine shop and stop in and talk to a manager about shops in the area. Even if he's not hiring he may be able to give you names of a few shops around there. All the small shop owners around here know everyone else.
Above all - WORK HARD!
Everything you do is a reflection of you.
Your reputation will be set in stone pretty quickly in a shop, so don't fock it up by slacking or doing 5hitty work.
If you genuinely try every day and do your best on every job you will not have any trouble developing as a machinist. It's not rocket science and it is getting harder and harder to find young men that are willing to earn their way to a career in this field. Realize it's up to you to motivate yourself and you are 10 steps ahead of the game.
Good luck, I hope things work out for you. I believe they will.
Apparently I don't know anything, so please verify my suggestions with my wife.