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-What are your ages?
-How long did you date?
-Who broek up with whom?
-Why did you break up?
-Could you explain your situation a little more?Thank you again for trusting us with your problem. Please reply as soon as possible so that we can finish answering your question.
You cannot really make him do something he doesn't want to do, he has to be on board as far as wanting to try the relationship again but he may just want some time and if that is the case then you will have to give him that time but you also have to tell him that you want to see if the two of you can work things out and if he says no then that is your answer but if he seems unsure then you may have a chance but you are going to have to show him that you have changed in order for him to even consider giving the relationship another chance. If you were arguing too much then he may be afraid that it will be the same thing all over again if he were to come back. If you can show him that you want to be able to communicate better then maybe he will see that things could be different and may be apt to give you another chance. I would first tell him your plan about working things out and then if he wants it give him the space and give him food for thought at the same time so that he can at least think things over but your plan has to include how the two of you can get past the arguing and fight you did in the past and then allow the past to be in the past and not look back.
Only you will know if it is worth it or not but if you have that feeling of wanting to fight for him then do that but after you have given him some time to think about things and evaluate the relationship. You also have to be willing to find closure within the relationship if he decides he doesn't want the relationship anymore. If you feel the relationship is worth fighting for then don't live with the regret of not fighting for your relationship when you wanted to fight.
I think it's up to you to decide what move will make you feel more comfortable and happy, if moving back home since your break up seems what will be good for you emotionally and financially then don't hesitate to do so but if you have a good job there and a place to stay maybe you could give it go there but since you moved there to be with your ex and the relationship did not work out it might be better to move to a more familiar surroundings that you know the people and have a job waiting for you but you have to make sure that the relationship is definitely over before making any major decisions.
I would move home for the time being and occupy your time with your family and friends, you need to be some where that you are familiar with and with people that will keep your mind off of the ex boyfriend so that you can think about what you truly want and what will be best for you. I would wait at least a week before making any decision and see where things go with you and your ex and if things don't get any better then I would make arrangements to go back home and heal from this. After moving home you may find yourself happier and less stressed about things that have to do with the relationship with your ex and may be able to move on from this.
You're Welcome and if you need my help again don't hesitate to ask for me.