Need to confirm ancestry of Sir John of Galway

I am trying to research and confirm the family of Sir John of Galway.  We were told by a professional genealogist that the Tomamichel family came from his line.  He fought at Ball's Bridge against O'Brien of Desmond in 1361 and recieved the honor of knighthood from Lionel, Due of Clarence, the lord lieutenant of Ireland.He was given the government of Limerick as well as a house, garden and mill and street in Dublin named Galwey Lane now part of Dame Street.

Here is the rest of what I have at this point:

John De Burgo, younger brother of Ulick de Burgo, ancestor of the Maruis of Clanrickarde

John had 4 sons: William the father of Sir Geoffrey Galway, created a Baronet of Ireland by James I and later executed by same.

Sons Henry & Edward died in Irish Wars  remaining son: Geoffrey de Galway served as mayor of Cork in 1430 married Elizabeth, daughter of Lord Kingsale.  His son, Edward Galway, esq. of Dungannon in the county of Cork, married Mary, daughter of Richard Lavallan was mayor of Cork in 1455.  His son was Geoffrey and married Mary daughter of Maurice Roche and was mayor of Cork in 1488.  His son:

William married Margaret daughter of Richard Skiddy - his son - Edward married Anastasia, daughter of Stephen Coppinger, his son - Richard married Elizabeth, etc.

This was all found in Galwey, of Lota in the Genealogical & Heraldic History of the Extinct and Dormant Baronetcies of England, Ireland and Scotland by John Burk in 1999. 

At some point some of the family is said to have moved to Switzerland and adopted the name 'Tomamichel' based on the first to arrive. They combined his first and last name: Thomas Mickel.  There are still descendents there as well as in the US & Australia.  We've connected Switzerland, the US & Australia but want to confirm and connect Ireland.  (I've bragged about being Irish my whole life!) Any help I can get would be greatly appreciated.

Debbie Tomamichel