I'm not sure how to move forward if he does not want to go to counseling or couples therapy etc. It would work best if both of you presented a united front, i.e. willingness to work together on your marriage. From what you write, there appears to be a lack of communication. It will be difficult to 'fix' things unless you both communicate... Does he want the relationship to work? Do you?

Just a comment though. When e.g. you ask him if he wants you to go, and he says it's up for you. Why not be honest with him and tell him (non-confrontational) that what you would like to hear is "Yes", in other words you want to feel he wants you to come. Maybe he doesn't think he is doing anything hurtful / wrong. Likewise, when he flirts online - does he know you are upset etc. Just explaining things in a calm manner (no nagging, no tears etc.) might help. Also, do the same for him. You could (a) ask him what you could do for him, or (b) surprise him by doing what you know pleases him etc.

As to how to know whether to call it a day or try, the decision has to be yours. After 2/3 years together, if he is not willing to do anything about the issues at hand, it might be best for you to move on. But it really depends on what each of you really wants... Do you want to pursue this? Maybe you could go and see a counselor to talk through these issues etc.