I feel your pain and I think we've all been there. The part about putting to much pressure on yourself I think may be right. One of the things that worked for me, but it took some self-training, was to stop going into every match thinking I should win this, no problem. Just play. I developed the attitude that I wanted to go into every match and play at my top level, play my best, regardless of what my opponent did. No matter what, sometimes the other guy will make all the balls before I do. I can't say for sure but I think this might be what is meant by the phrase "play the table, not the other player". Then the next big thing I tried to incorporate was to know my opponent, even if I didn't know my opponent, for example - at their skill level what can I expect of them? So you play your opponent, but you respect the table. And finally, to play smart. High percentage shots and safes, don't take chances I don't feel good about, and always be prepared to have to do something amazing, outrageous 90 degree cut along the rail, the perfect defense with one ball on the table, a 4 rail kick or bank, or whatever. Hopefully you'll never have to do anything amazing, but it's a good thing to have in your back pocket. Most of all, trust yourself.
I always harken back to the Karate Kid for advice, "Trust quality of your skill, not the quantity" and something that I heard Minnesota Fats say in an interview one time, "Take easy shots, if you shoot all your easy shots, you won't have any hard ones left"
Just play your best every time, let the rest take care of itself