I still don't know my exact research question but I know I don't like the ideas my advisor pushes me to work on an publish asap. What are my options?
From an outside perspective, you are just getting started. Three months is just a warm up period. One part of me wants to advise that the doctoral study period is limited and you should do what you need to do to get through it and move on to other things. The other part wants to advise that it isn't fun to work on something you aren't interested in for a few years. Dilemma. 

But, if you intend to stay with this advisor, I suggest, pretty strongly, that you take his advice. He has more experience and a wider view than you do. It would be fine, in my view, to ask for more time to find a mutually acceptable problem to work on, but if you get push-back, I think you either need to yield or find someone else to work with. But, it may be that you can come up with an idea that he has some interest and competence in quickly enough that it works out. 

You will get the best help from your advisor, assuming you need it, if you work on a problem he is also invested in. It is possible, but harder, to work alone, but you still need his approval at the end of the day. If you can get by with minimal help and final approval, you can probably make a go of it, though it will likely take longer than if you have strong help. 

But you should look, also, to see if there is another local advisor available who has more compatible interests. You also want an advisor who will support your future career. Fighting with him won't get you that.