'Sort out' is fine, and, as Johnny says, you don't even need to say 'problem' : the phrase 'We need to sort this out' tells you that there is a problem that needs to be dealt with. 'Fix' is used for something that is broken, and needs to be repaired.

I find that, most of the time, I don't need to use the word 'problem'. So, I would say: "We need to sort this out." "Let's sort this out." For me, 'sort out' refers to problems between people, like relationships or grudges, etc. Problems that involve both people. I use 'fix' for problems between me and the environment, like a broken computer or automobile. Also for problems between people that are my fault. For example: "I lied to my mom. I need to fix this." "My brother and I fought last night. We need to sort this out." "I need to fix my broken computer." "I need to sort out things between me and my girlfriend." When I use 'sort out', I'm implying that both sides have problems. When I use 'fix', I'm implying that the problem is mine alone. This is just my opinion, though.