i used to be like that but i found that the easiest way to do both is just practice. theres no like magic way, but there are training exercises to do. for example first, master the strumming pattern with your "neck" hand covering the strings.. get that in your muscle memory.
-Then get the chords to be almost second nature and get that in your muscle memory so you can play without thinking like "A-Fm-Bm7... you get it.
afer that humm the melody of the vocals along with the playing of the song....
-finally youre ready
-the whole problem usually comes in when your brain has to recal both the words and the chords.. and throw a strum pattern in there and wow your brain goes crazy.
so my main advice is to practice the song and then understand at what point the chord changes (lyrically ) and go from there
but with anything it's Practice Practice Practice
---- you could also just ge a cute member of the opposite sex to sing for you while you play-- thats always a winner