Unfortunately there is no way to easily know what piece of software installed the typeface to your system. And as you guessed you do not have license to use a non-system font for purposes beyond the scope of the program which installed it.
If you are unsure whether or not you have license to use a typeface it is best to assume you do not. As you acquire typefaces from various places save them into a folder designated for them and have two sub-folders for typefaces you have license to use and those you do not, respectively.
To help with typeface management there are several programs available, some free and some paid, that allow you to sort, group, and filter typefaces you have installed on your machine. This could allow you to group the typefaces you know came installed on your system by your OS and for other software. This is however not helpful to this particular situation because you have to know what installed a typeface to group them this way.
Some other answers have suggested getting typefaces from websites that offer free fonts. In my experience many such websites offer mostly poorly designed typefaces—often blatant rip-offs of popular paid typefaces—with very limited character sets, poor or non-existent kerning, and have many other significant problems. There are, rarely, hidden among them well designed and full featured typefaces.
If no other typeface will suffice, I would suggest purchasing it. If you are doing this work for a client you can charge them for all or part of the price of it. If price is a significant concern many foundries offer small subsets of a typeface, usually broken up by weight, for sale independently from each other at a reduced cost.