Thanks everyone for your input! I appreciate all points of view! It helps me to analyze the situation a bit better and not go off the handle and do something I might regret later.
I think I just really get so mad because all my life I have been so quiet and pretty much let people walk all over me. But the past few years as I get older, I realize that I am not this weak little person. I refuse to be treated in a rude manner. So now I think I may over compensate sometimes and take things that aren't that big of a deal too big? Know what I mean? But I still am not happy about the situation. I know I am definitely going to speak with my landlord about the situation, very nicely and professionally. I am not saying anything to our neighbor at this point. I just hope the situation will work itself out on it's own. But from now on I think I will either put the trash can in a different spot or try to move it asap. I don't want to fuss with them. They are not worth it the more I think of it.
Again, thanks for your input!