Parents of William Linn/Lynn born 1734 supposedly in Antrim, Ireland

Hi folks. My maiden name is Linn. I am trying to find the names of my 5th greatgrandfather's parents. He was born in Antrim Ireland in 1734 ad came to America in 1771. I can't find the ship he, his wife Agnes, and their 3 children came over on or even where for sure they ported at. The information I'm finding in a book by Margaret Hull about the "William Linn Family From Antrim, Ireland" states the family landed in the country of Mexico in 1771. I am finding that very hard to believe . They ended up in Pennsylvania in 1772 . I believe they may have entered the country in Philadelphia and went to the small locality of Mexico, Pa. However, I have no proof of that. Agnes passed in Patterson Creek(Hampshire Co. WV. William remarried an Isabella Gibson(also from Antrim, Ireland) and had several other children including my ancestor, Gibson Linn. They eventually settled in Glady Creek in Monongalia(Marion) County, WV. William died in 1808 there. William also fought in the Revolutionary War--a patriot. As to his parents, Ancestry and Family Search for the most part have his parents listed as William Thomas Linn and Jane Addis. These are a completley different group of Linns. They are not his parents. Does anyone out there have any information on these questions?