No!! Don't give up!! You got this!!
As everyone has said before we all started out this way! You have been doing it such a short amount of time and it is no way an indicator that you are not doing well or going to get it. Its better to take your time and understand what you are doing and familiarize yourself with your patients rather than rush and make a mistake.
When I started in the LTC I was the same exact way, I took VERY long giving meds and I was frustrated and upset that. I had a total of about 39 patients. It was my first nursing job as an LPN and I was so overwhelmed. I decided that I needed to help myself instead of tearing myself down. It took extra time in the mornings and even after my shifts but I went through the medex and I familiarized myself with each patient. I even made a cheat sheet for myself where I notated who needed applesauce, who needed crushed, who the GT tubes were, etc.
As everyone said, the more you do the faster you will get and you will develop your own flow as well.
During those early months of working in the LTC setting I would come earlier than my shift just to acclimate myself to my med cart. I would make sure that everything is stocked and loaded, make sure that it was clean and organized to how I worked.
You can do it