Dreaming that someone killed you in a strange room means that you sincerely want to forget. Maybe you really want to get rid of the present environment, get rid of all the troubles in the past and completely change yourself.
Dreaming that someone is chasing you at grandma's house indicates that it is very likely that you have encountered some troubles recently and made you very nervous. If you are already in trouble, you should solve the trouble at hand. If there is no trouble, this dream is to warn yourself to be careful and avoid trouble.
I hope this helps.