Three weeks is not a very long time to learn to shoot a bow. You say you shoot worse when you shoot with both eyes open. Oftentimes if has been my experience that when a person tries something different, they shoot worse for a while. I have no doubt that if you really want to shoot left handed with both eyes open, you will eventually be able to do it accurately.
Now, is that the best thing for you to do? That is a harder question to answer. As Jim notes, in the majority of cases, it is better to aim with the dominant eye. Most people can learn to change from right handed to left handed (or vice versa) in a few days or a few weeks at most. Some, like me, like to learn to be proficient shooting either way. It is not only fun to shoot either way, it is better for your body, as it keeps your physical structure in better balance.
If I had my druthers, I’d have you learn to shoot a right handed bow, perhaps a little less than 50#, and stick with it until you become proficient. Then continue to shoot both ways with both eyes open. But this is not a question anyone else can answer for you. Some very proficient archers aim with the “wrong” eye and do quite well for themselves by squinting, closing, or just learning to ignore, their dominant eye.