You can get the links to your release in the iTunes download store and Apple Music (if you selected this store) as soon as you see "Live on iTunes" message appear under the checklist on the album page in your TuneCore account. They are labeled as "iTunes Link" and "Apple Music Link". Keep in mind, these links may not appear in your account until your release is actually available in iTunes. Sometimes, the link will not send you to your release in iTunes. This may mean your release is being reviewed by iTunes. Learn more.
You can also get a link to your release in iTunes by searching for it and right clicking over your cover art and clicking, 'copy link.'
If you have an iTunes link to your release that isn't working or only bringing fans to Apple Music you may have the wrong link.
In order to fix your iTunes link so it brings fans to the iTunes Music Store you will need to add the following to the end of your iTunes link: ?ls=1&app=itunes
Link to Apple Music: https://itunes.apple.com/us/album/blacked-out/id999999999
Link to iTunes download store: https://itunes.apple.com/us/album/blacked-out/id999999999?ls=1&app=itunes
Regarding the "live" status of your album in your TuneCore account, it can take up to one week from when your content goes live in iTunes and when your content is marked as "live" in TuneCore.
Unfortunately no other stores provide us with links to content. You can search for your music in other stores by going to their website and searching your artist name or release title.