It's an interesting topic actually. I think the situation has to fit. The odds weren't zero that you'd have broken up when you actually saw each other more often. Cuz that happens especially with fresh couples (and three months is fresh). If you see each other, you can compromise after a big fight. Keep your pride for yourself and apologize or compromize. The question occurs: How is this possible with LDR? In my opinion not really easy. Another question occurs: What happens, after you see each other more often again? On daily basis? After a LDR, who can assure that the situation goes better? It could become worse. People change.
But then again, the most important question is: Is the person worth it? If it's definitely yes, then you should just try and see how it goes. And you did well by trying and I wish you best.