I recently booked an Air China ticket on mytrip.com. Although I got both a ticket number and a PNR, the Air China website couldn't find the booking (even on the page that is supposed to show third party bookings). I tried checkmytrip, it apparently found the booking but complained about my name not matching the name on the ticket and refused to show anything.

My solution was to use the Air China app - I did have to sign up for their Phoenix program in order to do it (took only a minute or so). The app does show my booking, I could reserve seats for free, the app also lets you reserve special meals and buy add-ons. You don't have to credit your miles to Phoenix in order to use the app, I still see my Miles&More number in the PNR.

My regular German mobile phone number worked for the Air China app registration just fine.