You need more replies! This sucks! But it is actually unfortunately really common.. I'm sorry that happened but don't let that stop you!!! You can be a nurse there is something better there for you. Keep trying at hospitals and even at that home health thing, it is all experience. I don't think it is bad to leave it off your resume, you were just in orientation if it comes up somehow you didn't lie just say you were in orientation so you didn't put it. Lots of people get fired, your resume is not an all exclusive job history it is your selling point, so is your every contact and interview.
You getting fired, in a way, was not your fault. You are new, you are learning and they didn't give you a reason because they probably didn't have one. It could of been anything. Not to say you shouldn't reflect, you should think about what you learned there and how you can improve. But like I said, I dont know you or the story so I am guessing, you didn't do anything wrong nursing is hard. I wish we graduated and were ready to start work! Until then keep applying and trying to meet hiring managers. If that doesn't work out after a little while try snf, you will build your skills, time management, how to deal with limited resources, how to delegate and communicate with patients, coworkers, doctors, families. It's hard but it is a start after 6 months to a year you can build confidence and keep trying to get into a hospital!
You can do it! Take your time, it is not a race you will get to where you need to be. Surround yourself with positive words/things etc. It's kinda cheesey but I like to listen to "The Secret" and Joel Olsteen (on YouTube), I'm not religious but he is so uplifting!