My sessions are full of conflict, and I think that this way of working just isn't for me. My counsellor and I seem to be incompatible.

There is a difference between realising that talking treatments can be a challenging (even painful) experience, and being willing to put up with almost any kind of frustration or discomfort in your sessions in the hope that it is doing you some good. You may be sticking it out because this counsellor is the only person in your area, and you might be unsure about what other alternatives are available. Whatever the reason for the difficulties is, talk to your counsellor about your doubts. It may be worthwhile sticking with the therapy if you are getting at least some benefits from it, even if it has its bad side.
However, if you have tried to discuss this with your counsellor and it has got you nowhere, or if it seems that you cannot do any more good work with the person right now, consider your other options. A different approach may be best for you, even if you have to wait. There is no reason to keep going with something that is not working.