First, I would say relax and not worry about it because you are most likely a beginner and are not working in the same way that professionals would do. That is, the production is not as effectively done, and the acting, therefore is not as effectively done. Second, If you mess up because you get embarrassed and laugh, then shoot it again, that's what the pros do. And they do exactly that--they giggle and break character. Third, you are an untrained actress, inexperienced outside of home made and school videos. It takes a long time (years) for actors to learn to be perfectly comfortable doing intense scenes. The best thing you could co is to be in some school plays and get more acting experience. Finally, putting yourself into the imaginary circumstances of the film and doing the role is something you need to concentrate on. Use your imagination to create the situation and characters of the film, then stay focused on that so you don't think about yourself being anything other than the character. This,of course, sounds easier that it is to do. But with practice you can become quite good at it.
One of the things an actor has to do is reveal her emotions. You have heard of good acting being vulnerable? That means that the actor shows his or her true inner emotional feelings. Sandford Meisner, perhaps the most famous of movie acting teachers said it takes twenty years for actors to finally be able to do his technique which accomplishes what we are discussing here. You have to be able to be so involved in the moment of the scene that there is nothing in your head but the moment. You never think about the fact that you are acting and there is a crew there. You just do the scene--you just react honestly and without inhibition to the stimuli of the scene.