I have seen many people been really affected when this happened in their private life, as well as in their work place.
When it is not managed in time, it can become very disproportionated in relation to the initial disagreement.
Conflicts are sometimes necessary because they are one of the ways you can affirm your personality. So don’t systematically avoid them.
But there are many other ways to affirm your personality as well, so don’t let it become a habit. And keep in mind that conflict which lasts, can become a mental prison. It takes all your energy and thought, and prevents your light from shining through.
Take a pen, and write on a paper when this started, and why it started.
If it started a long time ago, you maybe have forgotten why it started. ( Some people stay so long in conflict that they sometimes forgot the reason of the initial disagreement). If that is your case, it is really time to change.
Why did this started. Question yourself, is the motive so important that you have to lose all your energy on it, that you take the risk to compromise your credibility ( or objectivity)?