Many of my students have commented that they get nervous when playing in front of people and sometimes even in a lesson they say that they feel they can play better at home. This is a very common thing as when at home you are in a familiar and relaxed environment and your sole focus is on the music. As soon as you start thinking about someone watching you then the music is not the only thought in your head. Some people will have an adrenaline surge or sweaty palms and shaking hands. Having these feelings is very normal, you will overcome this but it takes a little time.
The more you play in front of others, whether it is in a lesson, in front a friend or a family member the less the severity of performance anxiety should become. If you can acknowledge to yourself at the outset that this is a normal step in the learning process this can be very helpful to your progress.