I am new to playing the low D whistle (Dixon duel whistle/flute), but have been playing the tin whistle (Clark) off and on for awhile. I’m having this strange issue - - - when I first got the whistle, I was trying to figure out how to properly close the holes so the notes would sound correctly. My thumb would cramp up, so I took a break and knew I just had to work on a better finger position. Well, it has been several months, and when I went to try it again this evening, no matter how much I know I am pressing down on the holes completely, there is no note distinction - playing the whistle without any holes covered sounds the same as playing it with the 1st, 2nd, ect. holes completely covered. I feel like such a dork, and can’t figure out what’s wrong. A lot of people love this whistle, but I am just super frustrated right now. 
Any advice would be super appreciated.
The first question that comes to mind is: Are you using piper’s grip? It takes some getting used to (especially if you’ve played the standard “high” D whistle previously), but once you get familiar with it, that should make a difference. From what you’ve described, I’d guess that either you’re (1) overblowing, (2) not covering holes well enough, or (3) both. Try starting with B in the first octave (xooooo), and work your way down to D in a descending then ascending scale. See how that goes.
Also, if you haven’t got a copy of it yet, consider ordering ‘The Low Whistle Book’ by Steafan Hannigan & David Ledsam. Lastly, if there’s an experienced low whistle player in your vicinity (a lot of pipers also play the low whistle), see if you can sit down for a lesson or at least to get a few pointers.
By any chance is there a thumbhole (for the C-nat) on the underside of the tube? If so, it needs to be covered, either with a thumb or tape. The problem you describe indicates a complete loss of tube integrity. It could also be caused by a crack, but I don’t see how that could be the cause. If it’s neither a crack or a thumbhole, check the joint where the head connects. If that is loose, you’ll get the same effect. You can check if this is the problem by wrapping some tape around the joint.
It would be beneficial if you were to post a video, too…
Pat
If there is no C-hole on the back, or crack, try blowing with no fingers and then adding one finger and then two, et c.
As Stiofan said, the Piper’s grip will most likely be necessary in order to cover the holes properly.
That is, don’t use your fingertips to cover the holes: