I started with a pretty extensive musical background as well, which is a big advantage.
The tin whistle is great. It might be the easiest instrument in the world to play basic stuff on, and of course in the hands of the masters it can do amazing stuff. It's surprisingly expressive and capable for such a simple instrument. Its a great example of the amazing things creative people can do with the simplest tools.
If irish music is your thing, you might consider trying the online lessons at the Online Academy of Irish Music. They start with lessons for the complete beginner and go to quite advanced.
https://www.oaim.ie/In general it's probably better to find a teacher, if that's possible or convenient. There's a beginner's guide here:
https://tinwhistle.wordpress.com/Edit: also it's almost certainly the case that there are two things you do wrong starting out
A: you have to seal the holes completely. Even a tiny gap where air can escape makes the notes fail spectacularly. Whether you use the tips of your fingers or the pads, you need to get a complete seal. You don't have to press hard, but you do have to close the hole. It takes some practice
B: you need to have steady and controlled breath, a steady stream of air. If the air stream you're blowing goes up or down a lot in force, the notes will not be steady
Basic practice rule: practice slow to play fast. Play whatever you are practicing slowly, with focus and attention.
Grey Larsen's book on the flute and whistle is very good and very through
https://www.amazon.com/Essential-Guide-Irish-Flute-Whistle/dp/0786686839/ref=sr_1_6?ie=UTF8&qid=1538049787&sr=8-6&keywords=grey+larsen+flute