Sorry to hear about your experiences. You are still learning. Don't be too hard on yourself; however, I did note that you are trying to "never leave an opportunity to learn anything". This is great and you are adopting a wonderful attitude towards learning, but you may be trying to do everything and cannot focus on anything by doing this.
In the beginning, just try and focus on YOUR basic skills as a new nurse. When you are starting a task, only focus on that task for now. You are not expected to notice EVERYTHING around you yet. That comes with time. You ARE expected to check your meds 3 times before giving it, ie right drug, right dose, right patient, right time, right route. It sounds like you know what you are supposed to do but fall short along the path somewhere. Try to stay focused. Your willingness to help others is sabotaging your own efforts in completing your task at hand.
Don't get distracted too easily. This will help you throughout your career. There will be many situations where distractions cause medical errors even to seasoned nurses. When doing something relatively dangerous do not let your mind wander or worry about other things. You are still in the process of getting your bearings so if you veer off from your task, you will not be able to find your way back too quickly and mistakes will happen. You are probably thinking about too many things at once.
Hope that helps! Good luck! Cheer up! Your attitude will take you far but just remember to focus on the task at hand.