The UK & Irish governments do share this sort of information for the reasons stated earlier. In any case the "denied entry" stamp is rather a large giveaway and may lead the airline to deny you boarding.

I wouldn't risk travelling to Ireland until you sort this out as being denied entry a second time will really make a mess of your passport - as well as thoroughly destroying any chance of being allowed to live in the UK in the future if you do get married.

Note that if you eventually do get married then you will have, under EU law, the right to live and work anywhere in the EU EXCEPT the UK - assuming your BF is a British citizen. For the UK you would need a visa