Watch the stage when your favorite band is playing. Odds are that if the lead singer is playing a guitar, he or she is playing solos, riffs, and leads only when not singing. Most of the time, if the lead singer is playing guitar, he or she is doing a pretty straight forward, repetitive strumming or picking pattern while singing.
I don't say this to discourage you from trying to play and sing simultaneously, but more as encouragement that even the elite musicians don't try and do it all. They let other guitarists play the fill in riffs and the screaming leads (most of the time). Take a lesson from that. Keep your playing simple while trying to sing. It's what the pros do.
Also, both singing and playing while keeping time and thinking ahead to what is the next line and chord change and are you getting to the bridge yet and so forth requires deep, intense concentration. Skills aside, just learning that intensity of concentration requires practice. Then you add in the effort to learn the musicianship skills, and you're understanding why many people who go on stage practice for hours a day, and that doesn't include the hour or more they spend doing warm-up exercises.
The answer isn't just practice. It's practice a lot while keeping your expectations humble. Record yourself so that a month from now and two months from now and six months from now you can play the recordings and hear the improvement. You won't feel it or hear it day to day necessarily. Parents don't see how much the kids have grown (or are not as surprised by it) as the uncle who only sees them every six months. Same with practice.
Hope that helps. It's meant to encourage you to practice and to be patient with yourself.
- Zurf