questions on my meditation practice?

My goal with meditating was related to improving my concentration for academic reasons. At first I came across a method of meditating where I count out my breadth and avoid thinking of idle thoughts. I had a lot of success with this method and was able to focus much more but at a later point I grew curious on what happened if I didn't count at all or didn't pay attention to my breadth at all. So I repeated this process which was now easier just without any counting or attention. I again had success but my mind was very much blank at all times, it gave me some fright, I wasn't sure if it was going to be something harmful since I usually pick up on tiny details that relate to whatever I am doing but now my mind was just blank, so I stopped practising meditation as a whole for a while. I have recently discovered that a lot of things I have been attempting already exist so I am wondering if: - There are any better ways then what I have been doing to achieve higher levels of sustained concentration? - What end results I will face if I venture back into completely clearing my mind rather than improving its ability to focus through breadth counting? - If there are other components that seem useful to my goal that certain kinds of meditation can improve? - I also don't have much of an opinion on the forehead sensation that is commonly called a third eye but I can control it at will, I would also be wondering if there is anything particularly special about increasing the sensation or not? Any help is kindly appreciated. I have also been gradually resuming my breadth counting meditation with success. --- (edited to add:) I am happy and my mind is calm but it is filled with songs and memories that I like but are not related to the task I am working on and as a result get me distracted from it. As such I wanted to make my thoughts silent at will so I can keep focusing on tasks which make me less happy than my thoughts do.