I have followed a few threads on this site on the right speed for learners to play. The wisdom of the wise is always play slowly, get your technique right and then speed up. This is good advice, but it has a couple of problems with it. Most ITM just doesn’t sound right when it is played too slowly: you seem to have to wind it up to a certain speed before you get that “Ah! I see!” feeling and it makes sense. Also most people learn the whistle because they want to play with other people and it is frustrating to have to put in ten years apprenticeship before you can play in a real session.
So I want to suggest whack on the old Altan CD and play along but don’t try to play all the notes. A lot of ITM tunes have a sort of skeleton tune inside them with the rest being ornamentation and it is often possible to simplify them to the point where even beginners can play at speed. It might not sound great on your own, but add a few other instruments and it’s OK. before long your fingers start twitching to do a few diddly bits and you’ve got the whole tune anyway.
The other advantage of this method is that if you crank up the speed beyond your abilities you have to “use the force”, ie, you have to switch off the part of the brain that is trying to work out what combination of fingers you need for F# and just go for it.
You need to practice slowly as well, of course you do, but I don’t reckon it does any harm to have a good blast at top speed in the privacy of your own home. You were doing it anyway, but I just want to say in my opinion there is nothing wrong with it.