Apple ID password problem

I changed my Apple ID p/w a few hours ago, while on my iPad. Seemed to work OK - I didn't get any msgs and/or errors. I have no problem closing & re-opening my iPad, which I assume means Apple ID is satisfied with my new p/w. I recently tried to open iTunes, and I was asked for the Apple ID and password. That's understandable, except that it would not open iTunes. Instead, it gave me a msg that there seems(?) to be a problem with iCloud. No other info is given! Consequently, it appears I can't open iTunes and iCloud. I now wonder what else I can/can't open. I always understood that Apple uses one and only one Apple ID - p/w combo, everywhere for all Apple devices & system apps. So, I don't have a clue what the Apple security s/w is telling me when it says there's some sort of iCloud problem. Is it really an iCloud issue, or an iTunes problem, or perhaps a problem with my new password!? Or other?! Any suggestions please (short of advising me to restore my iPad to factory settings - painful/frustrating undertaking)? BTW, I've discovered this problem while on my iPad. I also have an iMac (High Sierra) on the same LAN as my iPad. But I haven't yet checked to see if this problem occurs on the iMac too. Thx.