I grew up being taught to do everything right handed . I started shooting a bow at 8 years old and could hit things very well . Started hunting with a shotgun at 16 and did very well with that too .
BUT at 21 I wanted to shoot copetitive combat pistol . A friend of my fathers who was an instructor for our PD agreed to teach me . I hadn't even sent 6 rounds down range and he stopped me and had me do the domanent eye "test". He told me I was left eye dominant and even though I thought I was a pretty good shot , if I wanted him to work with me , I would have to learn to shoot lefty .
The next few weeks were very awkward but my accuracy improved tremendously over the next month .Like I said before , I thought I had been a pretty good shot . Now I felt like Doc Holliday !
I decided to try the same thing with archery and borrowed a lefty recurve . Like with the pistol , at first it felt very awkward but after a couple hundred arrows I was a convert for life . I had always been an instinctive shooter and still am (57 now ) but the improvements in accuracy were astounding once I got used to lefty .
If you can invest the time and change of equipment , IMHO , it's well worth it.