So you're the same as me then. I am right eye dominant but left handed.
From what you've said, you might only be slightly right eye'd (if so, that's the same as me too) The trouble with eye dominance is it's not a simple matter of one eye or the other, it can be a matter of degree. Also the dominace can move about. Say if you're tired for example.
When I started shooting, being left handed I bought a left handed gun and shot OK. I used to "dim" my right eye (half close it) which forces the left eye to take over. I have also owned and shot right handed guns, but never too well to be honest.
Having recently bought another left handed gun, I have had a lesson with Carl Bloxham, he got me to smear a little vaseline on the right lens of my glasses, I can still see through it, but agin it has the effect of making my left eye the dominant one. Well it seems to work as my scores have gone up significantly (more than 20%) My plan is to get a little patch fitted to my shooting glasses (I have just bought a pair of distance glasses just for shooting) which will effectively replace the vaseline. But that's me, and not necessarily right for you.
The fact is, eye dominance is a complex issue and no one one here will be able to guide you specifically without at least seeing you shoot and or checking you out.
In short, if you have any doubts over your eye dominance, and have any ambitions for shooting well, you'd be best to get that sorted properly before doing anything else.
As HDAV said, as a newbie. Had I been properly informed about this, I should/would have learnt to shoot from my right shoulder. But you really need to be certain of your dominance issue before going down that route.