I make my music with LMMS a free cross-platform desktop app (link). If you do not have some sample libraries (tool to make music in music apps) I would recommend Fluid_R3 soundfont (.sf2 file); it is decent, free, so-called general midi soundfont; you can find it in many places over internet it (here for example). You can use soundfonts like that in LMMS using it's soundfont player - I think it is most fast and easy to use instrument if you are new.
But really you will be hard pressed if you are new to music making and want to take this route of music making for this jam. I use this software but I have been making music on computer for like 10 years and used more complicated software such as FL Studio (commercial app) in past too. Also figuring out how to make music that loops seamlessly in your game can also be difficult if you are new to music production.