Piperdbh,

In almost all cases, there is no such thing as a family coat of arms. The purpose of coat armour was to identify the wearer on the battlefield when a helmet would obscure his face. Because families tended to go into battle together (even on opposing sides), it wouldn't make much sense for them all to carry identical shields, wear identical "coats", or bear identical crests.

Some nations or areas within them have, for various reasons, ceased to grant, record, or protect individual coats of arms. In some cases, coats of arms in these places have become "family" coats of arms because there was no longer an authority to officially grant or determine appropriate differences for the individuals that made up such families.

Because Scotland still has an heraldic authority, it would not be appropriate to use Scottish "family arms" so often hawked by tourist shops. These arms, in most cases, are the arms of the clan's chief and are his personal property. Even if nobody is officially recognized as the chief, that could very well change in the future as "missing" heirs come out of the woodwork.

The chief's arms are, generally, actually more simple than those of other armigers because those relatives of his in the clan will bear arms that have been differenced to distinguish them from the chief. Since the 19th century, a codified system of coloured borders, changes to dividing lines, and symbols has been used in Scottish heraldry to show these differences, though other methods had been used prior to this.

The arms that you describe, though I don't recognize them, sound simple enough to be the arms of the chief of your family name. If you're interested in your own arms you have two options - if your surname is Scottish and you can prove a familial connection of this name to a native of Scotland, you can petition a grant of arms from the Lord Lyon King of Arms in Scotland who will work with you to difference them appropriately. If you cannot prove a genealogical link along that line to Scotland, you can use the chiefly arms as a basis for your own and, if you choose to do so, register them with another heraldic society or office (the American College of Heraldry, the Bureau of Heraldry of South Africa, etc.).

I hope that made at least some sense!