You can install it through CReative cloud app.
1.launch creative cloud installed on your machine.
2. On Apps panel it will show Indesign CC. Click on install.
If you don't have creative cloud installed on your machine , go to https://creative.adobe.com/ and download InDesign CC from here.
I have Creative Cloud and did try to install it again from there (which is where I first installed it from). All it says is "InDesign is Up to date" as if it's still on my computer. I tried starting from the Home menu and still no success.
Ok. Quit Creative cloud(not just close) and then re launch it. Now it will shown InDesign as avliable to install.
If this does not help, go to the CC app, change the app installation language. Now you can install the problematic product in a different language again. This will also add lost unistaller components. Now you can uninstall it again correctly with the uninstaller, change back to your language and install it correctly again.