Do I even like doing research?
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