It’s like sitting in a chair and rubbing your belly with one hand while patting your head with the other. Then deciding I'm going to swing one leg and stomp the other while rubbing my belly and patting my head. Adding singing is like adding your legs, in time it can be done, but it will take time.
It would help a lot if you didn't have to think as you change chords; it would give your brain more time to process the other thoughts. So start simple and add as you can.
At this point it really doesn't matter if you’re playing a real song while singing real words to that song. You need to get your mind use to doing the things at the same time. So play an Am7 to a Dm7 over and over and make up words as you go and sing out loud. Once you are more use to doing it, start playing a simple real song with real words. I picked those two chords thinking you play them more often than an open G and an open D. If I'm wrong, start with whatever two or three chords you can make the fastest without thinking.
