Relax! The first year out of school is so difficult for so many reasons! I didn't have med errors but there were numerous times some of my meds were passed 'late'. And you know what? Oh well. It's better late than never and better late than when someone should not have gotten something. It got better with time but wasn't until much later that I became comfortable. I was just becoming comfortable when I left my job on a med surg unit for the OR. But the OR is something I could not pass the opportunity up.
I am sure that had things been different, or had I worked long enough I would have made a mistake like that or perhaps worse. I am OCD about everything and will recheck vitals myself if it's been more than an hour since my tech took them. It is important to check and recheck and check again whether it's orders, vitals, meds to give or documentation. There's times I have caught a doctors error before it could affect the patient. It happens. You learned something. Move on and it will get better. I will say this - I came awful close to making an error on a few occasions. I can easily see how I could have not caught something and therefore made an error. This is a learning experience. It really will get better.
Also, like others have said, four weeks is too short for orientation. I'm sorry, it is. Six weeks was too short at my first job and I got an extra two weeks (even with those extra days it was rough being on my own). They reluctantly gave it to me, and guilted me about it relentlessly. My manager and my educator just kept saying 'The first year is so hard, it'll get better you're doing fine.' It's easy to want to say that, but really hard to hear it as a new nurse. I felt like they brushed my concerns off without much consideration. It's hard to work through the role adjustment to being independent when you're concerned about whether you got proper orientation or if it's just a confidence issue. It doesn't help if (as was the case in my first job) your coworkers treated you like you were stuck on stupid for asking questions or voicing concerns about anything. My second job I got six weeks but had much better preceptors who knew and followed policy...and I'd been on my own a while at my first job.
Do you have an educator that works with your unit that you can speak with and discuss your concerns? Maybe they can help you assess your strengths and weaknesses and determine if you're really ready to come off orientation. They may help you articulate your concerns better to your manager. I know you said your preceptors and charge said you were slow... It's easy to say 'Oh, you're slow' But what are their suggestions to help you become more efficient? Can you ask them for suggestions? It's a hard transition but it will get better.