In relationships, we need to accommodate each others' mistakes because we are not perfect. Thus, we should forgive each other and give each other another chance. However, when a partner isn't willing or doesn't bother to correct his/her mistakes, it is usually wise to bring the relationship to an end because it will no longer be a thriving and healthy relationship.
The fact you found out he was chatting with someone in a manner that wasn't normal, then he was being unfaithful to you. In such a situation, when a partner realizes her boyfriend is cheating on her, she might not react positively. Thus, the reason you were harsh on him.
What you need to do now is to give him space. Not only him but also yourself. Why not send him a message that you are terribly sorry for how you reacted and you want this to come to an end. Let him know you love him and you will be waiting for him. Then, exercise no contact rule - do not communicate with him for a minimum of two weeks as it will give him the space he needs. After more than 2 weeks you can decide what next move to take as you will have reflected on the relationship. For instance, if he does not respond during the silent period you may call him. When you do so he may have cooled down which is a good indicator the relationship will be renewed.
If he responds during the silent period it is a good indicator he wants to continue with the relationship.