For your information here are two excerpts taken from "The Oxford Companion to Local & Family History by David Hey"

"Coat of Arms ~ Distinctive heraldic bearings. The name is derived from the 13th-century fashion of applying armorial bearings to a surcoat. See Thomas Woodcock & John Martin Robinson, The Oxford Guide to Heraldry (1988)"

"Heraldry ~ The origins of heraldry are obsure but can be dated to the second quarter of the 12th century in different parts of western Europe. The adoption of colourful devices on shields can best be regarded as a military status symbol that was popularized by the pageantry of tournaments. The first documentary evidence fo the practice comes from the knighting of Geoffrey Plantagenet, Count of Anjoy, in 1127.

The simple patterns of the 12th century became increasingly complex in later times. The rules and terminology of heraldry were laid down during the 13th century.  By the early 15th century the Crown was attempting to control the use of arms that did not date from time immemorial. The Heralds formed part of the Royal Household and were incorporated as the College of Arms by Richard III in 1484. Their county surveys - known as Heralds' Visitations began in 1530 and continued until the Glorious Revolution of 1688. Major surveys were made in c.1580, 1620 and 1666 and minor ones at other times. Many of the records of county visitations have been published by the Harleian Society or by county record societies. These are a useful source for pedigrees of families claiming the right to bear arms. The Ulster King of Arms conducted visitations between 1568 and 1649. In Scotland Lord Lyon King of Arms conducted visitations only for specific purposes.

Arms are hereditary and therefore of great use to genealogists in elucidating family trees, See, for example, Philip H Blake, "The Early Derings", Archaeologia Cantiana, 112 (1993). However, the mistaken or unauthorized use of arms causes confusion. A common mistake is to assume that all people with the same surname are entitled to the same coat of arms. A knowledge of heraldry is indispensable when studying funerary monuments, stained glass windows, bosses in church roofs, etc, See Thomas Woodcock and John Martin Robinson, The Oxford Guide to Heraldry (1988).

.....So if you descend from a poor Irish family like mine, then it is very unlikely your family having their own heraldic Coat of Arms.