"The person who wrote me trademarked my business name for similar products last year. I've been in business locally for five years, and online nationally and internationally for about three. "
Assuming the one mark would be confusingly similar to the other...
Ultimately, rights in a Trademark are created by use in commerce. And, the person using a mark for a longer continuous time period has superior rights to a person using a confusingly similar mark for a lesser period of time. So in short, so long as your use was first, and continuous, your rights to the mark are at least equal to the other party. Now, that being said, just because a person filed for trademark protection last year doesn't mean that they only began using the mark last year- they may have a use that dates back many years (and that may even predate your first use).
So, if your first use in commerce predates theirs, and you've continuously used the mark in commerce since, then they cannot sop you from using your mark (doesn't mean that they can't try, just that if they were to try to stop you in court, they would be unsuccessful). Now if their first use in commerce predates yours, and their use is continuous (was it filed at the state level or the Federal Level (before the US PAtent and Trademark Office), they would likely be unable to stop you from using your mark. IF you have been using your mark in commerce for 5 years, and their use is greater than 5 years, they would likely be estopped (prevented) from stopping your use of the mark.
Essentially (and answering another of your questions), a trademark holder has a duty to police their mark (i.e., research whether others are using a confusingly similar mark), and if discovered, to stop the other from using the mark (again assuming the 'other' is a person using their mark after your first and continuous use). IF you fail to stop another for a period of 2, 3 or ESPECIALLY 4 years, then they will have earned rights to use the mark in their established territories. And the opposite is true, where if another Sr. User (entity using a mark longer than you) have failed to police their mark, they cannot after several years come to you and all of a sudden tell you to stop your use.
Good luck. Search Common Law Rights (or CL rights), Estoppel, likelihood of confusion in this board for a whole lot of valuable information!