If the person that is annoying you in your dream is someone that you are familiar with in real life, it usually means that you find them generally annoying in real life. If this is something that you already know, or you are painfully aware that this person annoys you in real life, it may be time to take some defensive measures when they start to infiltrate your dreams. Perhaps there is a way that you could avoid them or at least see less of them. If you could get them out of your physical presence then you would stand a good shot of getting them out of your mind too. It is all about having the discipline to simply forget about them, or the cunning to get them out of your hair on a more permanent basis.
If you are unable to ignore the problem or to defer it, then the best course of action might be to try to just talk to the person that has been annoying you so much. Sometimes the worst problems or the seemingly most difficult areas of your life can be solved with a simple conversation. People generally do not try to be purposefully annoying, so if you notify someone that what they are doing is annoying to you, assuming they are a good person, they will usually try to curb their behavior so that does not interfere with your ability to work, or whatever situation it is that you are in. Don’t let your frustration go unheeded by you or anyone, it won’t be good for any party if it builds up in you for too long.
Sometimes when you are annoyed by someone in your dreams, this does not have anything to do with the person that is annoying you in your dreams. Especially if you have been having a rash of dreams lately where you have been annoyed by others, this can mean that you have been generally irritable lately then this dream can act as your warning that you need to stop. You are going to take yourself over the edge if you keep constantly worrying and letting every little thing get on your nerves.
Contrary to letting things get better with time, they will only be getting worse if you do not make a conscious effort to relax yourself. As much as you would like to blame someone else for annoying you, the fault cannot be laid squarely on them. You must also expect to take some of that blame because it is not only about them annoying you but about you being annoyed by them. Try to do some meditation when you are on your own, control your angry tendencies and don’t let yourself get overexcited. This will lead you in a greater path towards happiness.