Welcome to the world of Nursing. Most are knocked down bc it was not what they imagined. 3 months a brand new nurse and burnt out already Maybe you should look into a diff degree than a BSN. All a BSN will do is help you with grad school. Also don't feel bad about not getting med passes out an hour before and after. I have worked med/surg for 9 years and sometimes it takes me 3 hours but hey they were given right? You have to do what you have to do and sometimes schedules meds have to wait unfortunately.
Look into something different to try. Maybe a doctor office will be more of your thing and speed. Hospital and LTC nursing is very hard. And I have spent many days crying over it but I love it too.
I am so sorry you are overwhelmed. Maybe you could talk to your manager. Unless you don't think that will help. Also staffing and not having enough nurses to work is everywhere. And in most cases they do have enough to work but it is the budget that keeps nurses well staffed and safe and not stressed. Money is evil.
Try something different. Don't give up just yet. See if something else fits you. Maybe LTC is not your thing. I know its not my thing. M/S is. I live for it. It is fast paced, challenging,,but rewarding in some ways.
So chin up. Start looking for something that will not make you miserable. you should not be burnt out or have bad feelings only 3 months into nursing. Sounds like the job more than you. Keep on trucking! Apply for things that are interesting to you. And don't give up you just haven't found you niche yet. Hugs to you.