Hello
You've already been given wonderful advice, but couldn't resist to write something myself!

Firstly, what you are going through is sadly quite common amongst all sorts of performers (and non performers) but actually there is plenty of literature and coaches of just "people", as Dima suggested, out there who can be of help. Moreover it is something that can be changed, there are many ways to improve on it from all sorts of different angles. I will give you what I think could work, but more than that, I would encourage you to look out and find other ways. From the top of my head I can recommend a wonderful blog: bulletproofmusician.com or The Inner game of Music book. (I have an even better book for my taste, but not translated into English yet, if you speak Spanish let me know.) And there is so much more out there on performance anxiety, not only music related, but for example sports related.
Anyway. Here we go:
You say you "know" that is all in your mind and the way you think, and yet you continue thinking that way. That has to change. And you can change it, none else can. Specifically you mentioned that making mistakes is a "no-no". Whilst none wants to do mistakes, thinking about hitting the write notes when performing just inhibits you more, and you have the "voice" inside you creeping you and telling you all sorts of negative things that will just worsen your playing. Steps to follow. [it would be most beneficial for you to understand why you don't allow yourself to do mistakes, why it is so bad. Why it can't be as it is now. But this is maybe more than I can chew at the moment, so I will keep to specifics]
During practice time (on your own): Anytime you do a mistake, tell yourself IT'S OK. and SMILE. And let go. The next step is of course to look at what you were doing and correct the mistake. (Didn't you know the harmony or the notes? Did you misjudge a leap? etc Be rational and objective. Any thought of "I shouldn't do this mistakes" blabl, forbidden. Don;t allow your mind to walk there) But free yourself from the thought that mistakes are "bad". They tell you where you need to improve. You should be thankful to them. Everyone does mistakes! Is part of the human condition. You really need to accept this.
Secondly, is necessary to understand that when we practice we are "building into" the body and our subconscious all sorts of information that will be retrieved in a performance. However the moment you start judging yourself during a performance you are inhibiting that process is like suddenly you are putting all sorts of obstacles in the way. When you perform you need to listen to the music and let go and let do.Let the music happen from inside you.
It might be that you find switching your inner "voice" very hard, I would suggest to meditate. First 2 minutes, then 5, then 10. Every day to keep a calm and "clean" mind that is able to focus without disturbance at will.
When you perform in front of people try to breath deeply and calmly, and tell yourself that you are going to try to ENJOY playing as much as you possible can! Any second at the piano where we are not committed like that, is time wasted. Don't want to "impress" and don't play to receive compliments, that only sets up expectations and pressure in the wrong places. Play because you love doing it, because the music is so wonderful, and because the physical act of playing the piano is wonderful as well! If a mistake happens, keep breathing, and tell yourself "it's ok" and smile

(internally if you are playing a funeral march hehe) and keep doing music.
If you feel you need to go through a more "lengthy" process of getting ready to perform think and do the following:
Choose a note (let's say E,) and a fingering, (let's say 3 rh). Right, now invite your family members (you trust them enough to tell them this is an experiment from a crazy Spanish pianist). Sit at the piano, with full intention. Like in a concert, as a matter of fact get your best shoes and a suitable concert attire. Sit down, breath, feel the space. Feel the audience. Play the note E
two options here
A. You get nervous: Keep playing looooong note E (only E, only 3 finger-or as you have chosen), put the pedal. Listen to the sound. Keep playing the note E until your body is completely relaxed, until you feel you could do this forever and ever even in Carnegie Hall. (Imagine you are in Carnegie Hall). Now, enjoy the power of the sound you are making. When you are very confident you can stop. But now anyhow. As a great concert pianist will do

Listen to the silence afterwards. Keep the feeling of security with you. When you perform in future aim to go into this comfort zone mode. After all, playing a piece of music is just having more notes than E, but the principle is the same. You can move your 3rd finger on E, so you can do all sorts of other movements with more practice and you are able to do them in front of and audience.
B You don't get nervous: (And feel this exercise is ridiculous, because of course you can play the note E with the 3rd finger anywhere in the world). Well, there you go, Keep that feeling of security with you.As I wrote above.
I would suggest you increasingly play for your audience harder and harder pieces, but I wouldn't just yet played for them the piece that you just started, or where you still are struggling in some sections during practice. And everytime you sit to perform, think about note E.
Hope it helps a bit!
Ps; Sorry for the long email