If this incident is on your license record, you are going to have trouble. I would suggest a different hospital and a different area of nursing.
That being said, don’t just apply and hope. Call the unit you are applying for and find out who manages it. Put in your app, but then go to the unit and ask for the Manager. Introduce yourself, shake her hand, hand her your resume, and then get out of the way! Basically, “Just wanted to stop in and introduce myself. I’ve applied for a position her. Here’s my resume. Wanted to meet you, but I know how busy you must be, so just call me at the number there when you have time. Look forward to seeing you again!”
Once you get the interview, it’s up to you to convince them you want the job and are the perfect person for it. If you have to explain the probation dilemma, be honest and don’t blame it on anyone. You may see it differently – but not documenting meds is a big bad no-no and a huge liability risk for anyone who gives you a chance. Make it clear that you know this and accept responsibility for it! You learned a valuable lesson the hard way. If you blame it on anything else – it won’t sound sincere, mature, or responsible.