I was with a guy for 5 years and we fought all the time. Our first fight happened because a "friend" of his tricked me into thinking he was bisexual and was receiving male porn via email. I don't know what your first fight was about, but I can definitely understand the crushed feeling. And hey, if you need to cry for 4 days then you do that. Don't let anyone tell you how you should and shoudln't feel. Sexual/emotional bonds may play some part in it but there are also people who would cry for days over a stranger calling them a name on the street.
I'm one of those people. Or at least I used to be. But getting back to the point... People definitely have different levels of sensitivity to these things and that's nothing to be ashamed of.
Well I've learned a few things about couple fights over the years. Some of these may not apply to you, but if I'm going to list one I might as well list them all...
One, if you're fighting
all the time then you probably shouldn't be together, no matter what it is you're fighting about.
Two, men and women fight differently. Men will generally be inclined to walk away from a fight so they can be alone and work things out in their own mind, while women will want to continue the fight without even pausing until it is resolved. (Trust me and give the guy his space.)
Three, hurtful words come from hurting hearts. If he gets in a good jab, instead of slinging one back at him, try to understand what he's feeling and respond to that. Look past his words to the feelings behind them.
Four, watch what you say. Words can do a lot more damage than we realize in the heat of the moment, and not everyone understands number three.
Five, never raise your voice. Try not to be defensive. It may take every ounce of strength you have, but this is very important.
Six, listen more than you talk. Even if he's screaming like a banshee and not making any sense, listen to him. If you have to then ask him to clarify some things so you understand. Even if he doesn't see it right away, in hindsight he'll know from the way you listened that you really do care about him.
Seven, "I'm sorry" and "Will you please forgive me?" are powerful, powerful words.
That's all I can pull from the top of my head right now. My fiance and I haven't had a single argument yet, but there were many times when we could have if I hadn't taken the above approach. Instead of blowing up and following my urges to lash out at him, I remembered to speak softly and make my point without getting defensive or disregarding his feelings. The results are awesome.
Hope that helps.