I won't speak to the presence of this sort of thing in either Bipolar or Borderline. /u/pema108 did that just fine, and I don't want to encourage anyone to potentially treat a person's emotional states or opinions or expressions as though they are only there because of the illness, and therein make the person more their illness than an actual person.

But I think the answer is glaringly obvious. If you both are unable to resolve conflict without not speaking to each other for days, sometimes weeks, you are not fit to be in a relationship with each other. When you wind up actually together, you can't just walk away for days or weeks at a time and saunter back in for a hug. You can't have explosive arguments about little things because little things happen on a daily basis and you need to be able to deal with them simply, concisely, and without biting anyone's head off.

The unfortunate thing for the pair of you, to add to the above, is that neither of you grew to know who each other really are at the start of your relationship. You don't know each others daily habits, you don't know every intimate detail of how each others days are spent, how you both handle stress, how you both handle being in each others faces more often than once every so often. Those are things that most couples discover from the get-go. And they're things that make or break a relationship - which is good at the start, not so good at the half-way point.

I would discontinue this relationship before it gets out of hand. Love is not enough to make a relationship work. There are clear signs that neither of you are ready or equipped to be with each other. And if either of you did make the move and the commitment and things did get worse you'd only find yourself in a pit of resentment, displacement, and conflicting feelings of needing to end things, but also feeling obligated and hurt at the prospect.