Get your CDL and keep your record clean and you will never want for a job again (unless the Mexicans invade the industry). It sounds like you got a good attitude and very little if any responsability at home. If you can, get out of your lease if you have one and just shack up with your parents when you're home, you won't be home enough to wear out your welcome
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After the first year you'll be in a much better position to write your own ticket.
The Schneider thing is odd, I admit. I worked for them in the late 90's and they were a pretty decent company, but guys got in with worse driving records than what you claim. Maybe they're tightening the screws.