Am I allowed to use an fps in opengl that I have been working on as a base for my game rather than something pre existing like unreal or unity? All of the visuals, mechanics, sounds, levels and other code needed to create the game would be made during the duration of the game jam.

Yes, anything is basically allowed since no-one can check it, there is a checklist of things you can mention during submission which is displayed on the submission which anwsers your question, it is a free game jam and you should be honest about what you create and did during submission and what was used. Have fun!