Are you hosting the file on a server or are you (gasp) carrying the file on a USB stick everywhere?
If you host it on a server then it sounds like FileMaker teams licensing is for you. You can install FileMaker on as many computers as you want, but only one can access the file at a time with your FileMaker file username and password.
Best to call FileMaker and discuss the options with them, there are a number of different licensing options.
Another option is that you could create a "runtime" if the file is not network based, and install that on all the computers and continue carrying around the main data file for the runtime as you are. I don't really advise carrying around or copying a main data file in any case though... Too many data risks.