I don't know if it's a denomination thing, but I am what you'd call henotheistic despite otherwise checking out with the "no other gods before me" thing. Anything may exist.
Are you something like mormon? I didn't know that there are christian(?) denominations that allow for the existence of other gods. I was raised catholic and my first of the 10 commandments was "I, the Lord, am your God. You shall not have any other gods besides me." So that rules out any other gods. Along with the continuation of the story where god outlaws idols and sends plagues and burns down cities for worshipping anything besides him.
But I think I agree. Technically you're just not allowed to worship them. They may exist. It'd be a bit strange since the bible goes on and on how god created all the animals, angels, satan, humans, does all the things and some get lengthy enumerations... but somehow they forgot to mention that other gods exist... Just slipped their mind as they were writing it down.
The commandment, when written as is, is "you shall not have any gods before me". The words "gods" and "before" probably cause some kind of misunderstanding, as the commandment has never been seen as blocking the acknowledgement of other entities to me. Relevantly, in ancient times, the entities in other traditions were acknowledged as saints or demonic forces recognizable by the papacy. Saint Brigitte, for example, is a specific saint tied to a specific figure worshipped as a goddess by the ancient Irish. Angels in general are notable for having powerful or effective qualities.
But if the literal meaning of one word is important, we have to factor in the original hebrew meaning. I don't know what it says. But you cant pick an arbitrary translation you like best. My translation of the bible with "besides me" is equally as valid.