It sounds like your realization wasn't that you put lives in jeopardy by violating the law and driving impaired, but that you risked your "career."

The legal violation will become a part of your past, as will the incident, but what you need to understand isn't that you put your career in jeopardy, but that you did a very foolish thing that risked lives, and showed deplorable judgement by electing to operate a vehicle in public while impaired (to say nothing of the choice to get impaired in the first place: pick up on end of the stick, pick up the other).

Your "career" involves employers trusting you with millions of dollars of their equipment and hundreds of millions of dollars of their liability. It involves passengers trusting you with their lives, and their children lives, and their parents, brothers, and sisters lives. What you're willing to do with a car is what you're willing to do with an aircraft; exercise poor judgment that puts equipment and lives in jeopardy. That's the realization. Your concern that it might affect your career should be far down the list.

Should you give up or stop flying for a while? No. Should you continue to reflect on this while you work on your certificates and ratings? Yes.

Applying for a job right now is irrelevant, as you lack the qualification. Focus on achieving your pilot certification and flight instructor certificate first, then concern yourself with applying for a job.

Most schools prefer their own students; do your training at a facility that has openings and adequate student traffic to keep you busy when you complete your training. Be honest and up-front with them about your background so that as you move toward certification, no one is surprised and everyone is onboard and comfortable with you.

In the meantime keep your nose clean, avoid even a parking ticket, and live in a way that you can show your determination and distance from your error. Actions speak louder than words.