Anger can be a complicated emotion, often being mixed with sadness or worry, but there are things that, depending on the cause, you can do to help yourself feel a little better.
Negative feelings towards another person can often not be helped, and feelings of guilt can occasionally surround them. If this is true in your case, know that it is completely ok to be upset with someone, but there are things you can, and should, do to resolve this in a healthy way.
Allow yourself to feel the anger. Sit with it for a while. How does it feel? If the anger is still fresh, then sit with it for a little bit. Just feel the emotion until it goes from an overwhelming feeling to something more manageable.
Identify the cause of your anger. what exactly did the other person do to upset you. Dig deep to find the root of not only what they did, but why it made you eeel that way.
Avoid judgemental thoughts or language. Making wide sweeping characterizations about people based off of one interaction you've had with them can do more harm than good. Alternatively, if you notice any patterns between this specific instance and others prioviously, note that.
Approach the person. Be incredibly mindful of an appropriate tone and position to take when dealing with other people. Approaching with respect and understanding is more likely to be effective in resolving the situation then an immediately hostile one. Let the other person know, not only about what they did or said, but how exactly it made you feel.
Focus less on "winning" and more on coming to a resolution. Things aren't always going to turn out exactly how you'd like, but one thing you can help to improve is the note you end on. Even if you aren't seeing eye to eye on the situation, try your best to find something that you can agree on and come to a conclusion on. Situations like these can be less than ideal, but understanding at least where the other person was coming from can help you avoid or better manage situations like it in the future.
Feeling angry or upset with yourself, whether this be something you did or said, is a natural part of life, but you shouldn't let yourself be hurt by it.
Everyone makes mistakes or does things they regret, but the most important part of that is learning and growing from your mistakes.
Avoid self-depricating characterizations of yourself, like calling yourself stupid or similar things. Instead, use this feeling to relect on what happened and what led up to it.
How likely is this situation to happen again? If it feels like just a one-off thing, then don't beat yourself up too much about especially if it's nothing too serious. These feelings can also include ones of shame or embarrassment. If that's the case, there's not really much you can do about it other than reminding yourself of the fact that everyone does things they're embarrassed by and overthinking it isn't going to help.
Think of if there's anything you can do to prevent something similar from happening in the future. This is most generally applied when talking about things like failing an assignment or saying something you didn't mean to. Don't get too down on yourself about anything in particular, instead, think more about why what happened happened and things you can do in the future to prevent it.
Lastly, remember that no matter whare these feelings are coming from, feelings like this are normal and while they may be unpleasent in the moment, things will get better.