First of all, you need to answer some important questions to start getting your ex boyfriend back.
Is the cause of the argument important enough for all the attention that it is currently generating?
Can anything important be changed by staying in the argument?
Is it even worth arguing over it to begin with?
If the answer is no to any of the above questions, let the argument go along with the tension and stress attached to it. Many breakups can be prevented or quickly rekindled if the argument can be settled or addressed at a calmer time.
The next step is to forget about how you are being perceived by your boyfriend or others. It doesn't matter what people think about you. Being concerned about how others perceive you will get in the way of who you actually are. Let your true self flow. This is the real attraction for your boyfriend.
Become emotionally distant from your ex boyfriend for a time. As the saying goes, "Distance makes the heart grow fonder", is applicable in this case. Let your boyfriend know that you are interested in keeping the lines of communication open but take it slowly. Keeping a distance will take the stress off the relationship and when you do see each other it will be in a calm and relaxed state.
Once you are together your situation can be analyzed for what it truly is. Most breakups can be easily undone if both of you have the calm and patience enough to talk things through. This is one of the first crucial steps in rekindling your relationship.