I received my 1st vaccination shot in Shanghai (I have the certificate) and the 2nd shot in Kunming (near chenggong) but I wasn't given any receipts or certificates of my 2nd shot.
Where can I find information about my 2nd shot received in Kunming? Is there an online database , App (doesn't show on alipay) or should I call the CDC?

There has to be a paper trail. What I would do is go back to the place(give them a call) and inquire why you didn't get a certificate. Each time I went I had to pay 100 RMB. I was given a receipt for that. In addition I was given a certificate showing what vaccine I received (Sino-vac) with the day/time/Name/Address/Passport Number etc.
I went to the Calmette hospital on Beijing Lu near Lin Yu Qiao. Got all three shots at the same place.