Upvote:1
Your UK entry ban is either 2 or 5 years, depending on whether the date of your departure was less or more than 6 months after the date on which you were either: • given notice of their removal decision • no longer had a pending appeal against that decision (appeal rights exhausted) https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/606970/GI-Re-entry-bans-v7.pdf#page5
If you don’t have the paperwork, you can make a Subject Access Request https://www.gov.uk/government/publications/requests-for-personal-data-uk-visas-and-immigration/request-personal-information-held-by-uk-visas-and-immigration
Jamaican nationals need a visa to enter the Republic of Ireland. http://www.inis.gov.ie/en/INIS/Pages/check-irish-visa The UK and the Republic of Ireland are part of the Common Travel Area; they share Immigration data which makes it highly unlikely you’d get one.