If a potential professor said he did not accept any more PhD students this year, could I reach to another professor?
If this is the US, then it is common for students to be accepted into a doctoral program without knowing who their advisor might be. You will be assigned an advisor by the department initially so that you get course advice, etc. But that may not be the person you actually want to work with. 

Once you are accepted into the program, you have some time to look around and match up with a professor who will be your dissertation advisor, dropping the old, temporary, advisor. 

So, no, you don't need to contact another professor now in order to apply. Once you are accepted you will want to attend to that, of course. 

Note that the practice varies by country, by university, and by field. What I describe isn't universal. In some situations you do need to know which research group you will be part of in order to be accepted, but the response you got suggests that the situation here is as I described.