Do I even like doing research? Currently, I am a part-time research assistant in the field of physics. My supervisor is brilliant and very nice. He always encourages me and says that I have done a great job so far. I don't know why I feel like I did not do a good job and I am very bad at research. I got stuck on something for almost three months with no progress at all, which made me start to dislike doing research. 

I was dreaming about doing an MSc. and a Ph.D., and because of those feelings, I am having doubts if I enjoy doing research. Is it that I did not learn well how to do research, or that it is not meant for me? Is it possible to like doing it again with time? I want help in answering these questions to know if a Ph.D. is the right path for me...
Two ideas that might help.

The first is that you are new at this. Like any skill it is likely to improve with practice and time. As you progress you get insights that lead to further insights. But those insights don't come at regular intervals, can't be scheduled, and are harder for beginners. Frustration is common. 

Second is that if you are really doing research then you are exploring the unknown and it is, well, unknown. Three months on a problem without success is not very long really. It is hard to predict how hard any given problem is. It might take years to crack any given nut. But it is also true that it isn't helpful to become so obsessive about a given problem that you ignore the possibility of progress on other, related, problems. That other work can lead to the insight you need on the harder problem. 

“If we knew what it was we were doing, it would not be called research, would it?” ~~Albert Einstein