There are actually quite a number of tartans recorded with the name "O'Neill," though none of them seem to quite match the description that you have provided.

In the International Tartan Index, tartan 2464 is an O'Neill tartan that was identified in Australia where it was being called "O'Brien."

Tartan 2663 is the one Linda Clifford designed and is woven by Strathmore.

Tartan 5536 is one identified in 1983 as being worn by a Pipe Band but the notes are confusing as to which one (possibly Co. Tyrone Pipe Band in NY).

Tartan 1810 is also attributed to "an American Pipe Band" but looks more like a dancers' tartan.

Tartan 5535 is called "O'Neill red" and is also attributed to the County Tyrone Pipe Band in NY.

As I said, none of these would appear to be your tartan at all. Specifically, none of them have broad blue bands, as you describe. However, in the notes for 5535, it makes mention of the fact that this tartan is the "same as 6360 O'Neill but minus one black line and two broader blue guards."

It sounds like this O'Neill that they mention, but do not show, may be yours. Problem is, I think the number was recorded wrong, because tartan 6360 is the Muskova tartan, one designed around 1980 by Bill Johnston for wear by those of Russian descent. It has nothing to do with any O'Neill tartan. So this note appears to be referring to some other O'Neill tartan that does not appear in the public version of the ITI (though they may have record of it in the full version).

If I were you, I'd email the details of your tartan to Brian Wilton, director of the Scottish Tartans Authority, and mention to him the notes in 5535, as I just did, and see if perhaps they can get this error fixed.