New Grad quit now what?

I was working three months at a rehab facility. Long story short it was incredibly unsafe- for the patients and for my license. I left on not good terms with the facility and am now searching for another job. I'm wondering if I should put some details about leaving this place of employment in my cover letter. The unit manager who I was hired with has 20 years cardiac experience from bringham and women's hospital is one of references and left due to the same safety issues. I really want to find a great supportive environment next, as I am still a new nurse. After submitting applications how soon should I call to check in on my apps? Also when is a good time to ask for a job shadow? Thank you
Say it wasn't a good fit. That is all