There is another Valentine’s jam currently going on, and I was wondering if submitting my project to that one as well would cause issues? Some jams forbid submitting the game for any other jams, so I’d like some clarification

The very first rule is "Your game must be original and created specifically for the Valentine Jam.". So whatever you create has to be made for this jam, but if you later submit it to a jam that allows participation of other jams, then it should technically be "legal".  I don't make the rules though, so don't believe me :D

I think you should go for it. I probably will also enter mine in the other jam