picking too deep on cord changes

As I am progress in my guitar work with cord changes i find my strumming with a pick tends to end up digging into the strings rather then weeping during changes.. This not only sound bad but my next strum tend to be off. I am using 4/4 time. I try different speeds but still have that pick digging. I know concentrating on cord to cord technique without timing with improve this situation. concentrating on proper picking tech is important. But i can't seem to be able to stop the digging. A lot of it is mental. I get more and more tense when it comes time to change cords. Any suggestions physical or mental would help

I have two suggestions.
Take time to just strum the strings. With your left hand mute the strings, then strum the strings. You take time to work just on making chords right? Spend some time just working on strumming.

Say 4/4 timing for 10-20 bars.
Strike the strings with the same pressure the whole time. The longer you can do it the better. Start with 1/4 notes then 1/8 notes. Change the strum pattern and do it again.

Once you get that down start changing chords as you strum. Not playing songs just practice changing chords while you practice strumming. Your mind will start trusting your hands to change chords while you strum and you will stop worrying about it.

Shorten your pick grip.. maybe too much pick sticking out. Even try without a pick.
Don't be worried about, it supposed to be fun..
What haghj500 says will work..
When you feel comfortable to go back to chords, used the easiest chord you can do. No chord change. Then find the next easiest chord.

I always like to use Am to E..