The language spoken in Ireland and in Scotland (where there are still about 60,000 speakers at one level or another) is the same language. It was taken to Scotland around 500AD by Irish settlers. They were a tribe called the Scotiae, and they gave Scotland it’s name. So Scotland is named after an Irish tribe.
(No-one is quite sure what the Picts spoke but in southern parts of Scotland the inhabitants spoke Welsh, sometimes called Strathclyde Welsh).
Gradually Irish Gaelic replaced whatever the Scots had previously spoken. And then English began to replace that. However Gaelic is a language with many regional variations and dialects. So the Irish spoken in the Glens of Antrim was noticeably different to that spoken in Donegal and that is different to the Kerry dialect. The Irish spoken in the Glens of Antrim was almost indistinguishable from that spoken in Scotland (so I am not sure I would fully agree with your teacher when she tried to distinguish between the two. They are not two separate languages. They are very closely related languages. When I did my beginners Irish course at Queens University in Belfast, the lecturer tended to refer to all the dialects as Gaelic, occasionally prefixing with Irish or Scottish if she wanted to explain any differences. There are differences in the way it is written eg the fada points the other way in Scotland but that is a much more recent development. Most native speakers couldn’t write anyway. They weren’t bothered).
It’s about 11 miles across to Scotland at the closest point between Antrim & Kintyre and folk went back and forth all the time. Writing in 1654, a Dutchman, Joan Blaeu described “Cantire” (Kintyre) and wrote:
“Today in the Irish language, which is used all over this area, it is called Kintyre, that is Head of Land. It is inhabited by the family of Mac-Conell, which has lordship but at the pleasure of the Earl of Argyll; they go regularly off to Ireland for booty in their light ships, and have occupied the small provinces called Glens and An Rata (the Route)”.
The Route is the area between Ballymoney, Ballycastle and the Giant’s Causeway.
In the 1850s people in the Glens would have spoken Irish (but with some English as well). There’s not much Irish spoken routinely in the Glens today, save in some schools, but it was widespread then. It’s a slightly different dialect from that spoken elsewhere in Ireland now, reflecting the fact that the majority of inhabitants were of Scottish origins, having moved to Antrim in the 1500s and 1600s.
According to "Antrim and Argyll: Gaelic Connections" edited by Wm Roulston (page 2): “Gaelic links between Antrim & Argyll lasted well into the modern period. As late as 1881, 65% of the population of Argyll was Gaelic speaking, and clusters of native speakers of Argyll Gaelic survived into the twenty first century. Gaelic faded from Antrim somewhat earlier, but the Ordnance Survey memoirs show a vibrant Gaelic culture in the Glens of Antrim before the Famine, 43% of Rathlin Islanders were Gaelic speaking in 1901, and there were still native speakers of Antrim Gaelic in the second half of the twentieth century. The Antrim & Argyll dialects of Gaelic were linguistically very close.”
There’s an article here about the use of Gaelic in Ulster:
“Native Gaelic-Speaking Protestants
There is much circumstantial evidence of Protestants who were native speakers of Gaelic, and other Protestants who became very fluent through everyday interaction with other native speakers. Many of these Protestant Gaelic speakers came from Scotland. During the plantations of Ulster in the early 1600s only ‘inland Scots’ were supposed to be settlers; this policy was intended to exclude Gaelic-speaking Highlanders, but failed to do so. When the Marquis of Argyll brought his troops to Antrim during the 1640s uprisings, most of them would have been Gaelic speakers, and many settled in Ireland when they had finished their military service. Overpopulation and the commercialisation of estates in Scotland also pushed people from Argyll to Antrim in the 1690s; sometimes the dispossessed were recruited for military campaigns in Ireland.
During the time of the Plantations of Ulster there was little difference between the Gaelic of many Scottish settlers and the Irish of the natives. The Irish of Antrim shared many features with Scottish Gaelic, and the Gaelic of Kintyre and Argyll was very similar to Antrim Irish. Robert MacAdam wrote in 1873:
Even yet the Glensmen of Antrim go regularly to Highland fairs, and communicate without the slightest difficulty with the Highlanders. Having myself conversed with both Glensmen and Arranmen, I can testify to the absolute identity of their speech (Ó Baoill 2000: 122).