How do I know when it's okay to tell someone I'm angry with them and when I'm just picking a fight based on a small disagreement?

If something bothers you enough that you become upset, you should let the other party know. You are picking a fight and not just standing up for yourself when you feel the need to comment not because you are impassioned about a subject but because you're trying to bother/anger the other party. So tell someone you're angry when you're trying to resolve your own anger, and don't tell someone you're angry if you're trying to lure them into feeling an emotion.

Think about what made you angry. If you did that same thing to someone else, would they get as angry as you?

It is always good to share your feelings in a constructive and caring way. If you feel hurt no matter what it is important to share it with the person that you are in a relationship with, be it your friend, spouse, parents or siblings. It is, however, the way the that you share your feelings that are important. Never attack the other person. Keep to the facts of what happened. Explain that you love the other person, but that you need to share your feelings. Talk about it in a rational, calm and loving way and look for ways to solve the situation that will make you both happy.

One way to tell the difference between a problem you should confront someone about and a minor disagreement that you could ignore is by asking yourself if it is truly causing a problem for you or a rift in your relationship and whether it is reoccurring. If it is something small that someone does once or twice that unintentionally irritates you than it may not be worth confronting them about, but if it is constantly reoccurring or causing a major problem, than perhaps you should explain to them your frustration.

Anger usually leads to disappointment in another person or yourself. You can ask yourself, "Am I just disappointed or do I disagree?" If you are able to distinguish between those two, it can help you tell.

You could try to put the problem to the back or your mind, and if you are still angry, then talk to the other person calmly. Being calm is the best way to deal with anger.

Open communication is always important when you feel strongly about something. Angry is a rather strong feeling however that can quickly escalate a situation so take time to calm down before discussing the issue. Once you feel less angry you can talk to the person and let them know that the situation did not make you feel very happy, and you would like to talk to them about this so it does not repeat itself. Try and also look at a situation from their perspective, did they try and make you angry or was it just a misunderstanding or assumption on their part?

Just tell them anyway, it clears up any miscomunications you may have during the argument. I have done this plenty of times

Whenever you are uncomfortable, you are uncomfortable. No one can tell you how you feel or if it is worth it or not. Small or large - these are in the eye of the beholder, it doesn't matter. It's always ok to express how you feel. Someone who is worthy of conversing with you will respect you for this, and people who think you are overreacting are not healthy to have around anyway.