I agree that it sounds like a push, unless you are seeing a distinct left to right slicing ball flight.
A lot of what causes a push has to do with getting your lower bady ahead of the clubhead and too far over your left side. In other words, if you are trying to swing too hard, you might be shifting your weight to your left side way ahead of the club, which is trying to catch up during your downswing. It causes the club to come through with an open face, but if your shoulder plane is good, it puts a good hit on the ball, so it goes straight right. This is not all bad because the upper body is where direction comes from while your lower body is what generates power.
If you get too far ahead and your shoulders rotate too far, you would see a slice instead of the straight right ball flight, , thus a straight push is not hard to fix.
When we hear the pro player tell us to "swing within ourselves", this is exactly the case they are referring to. Try to make a smooth swing and find the happy medium where your body and swing speed cooperate. The key element is to maintain your balance so your swing can be repeated virtually every time.
Spend a little time on the range where each swing doesn't affect the fun of a genuine round. Try to make some smooth swings with the driver and you might be surprised how far you can hit it without having to flex your muscles to the point that you feel a lot of tension.
Now in my mid 50's, I wish I had learned that lesson many, many years ago. I swing a lot easier now and still hit it about as far as I always did when I was younger.