It is possible that you are dealing with a type of verbal or emotional abuse from your parents. For example, calling you an “ungrateful bitch” is definitely a verbally abusive statement. Clearly you could use some help in dealing with this conflicts at home, however, it sounds like you are afraid of what your therapist will do if she knows about the dynamics at home. But FX wants you to remember that she is there to help you in any way she can and that it is important that she intervene on your behalf. FX would assume that she would want to either incorporate your parents into your therapy with her, or, if you would prefer, send the three of you to another therapist who will do family treatment while you continue with your current therapist for individual therapy. It is important that an adult intervene to talk to your parents about how harmful this behavior is for you and for their relationships with you. And it is important for you to know that there are adults out there who will want to treat you with respect and understanding and who will be there to support you during difficult times.
One way to approach this is that before you bring this specific issue up with your therapist, let her know that there is something you have been wanting to tell her, but that you have concerns. You can then explain to her what worries you without divulging too much information so that the two of you can deal with your fears about what might happen if you were discuss this with her. You can also talk about a plan of once you have told her, how to go from there is a way that will feel comfortable for both you and your therapist.
It is not okay how your parents are relating to you, and it is obviously and understandably having a negative impact on how you feel and on your relationships with one another. So please take steps soon to talk with your therapist about this so that she can be there for you with help, guidance and support.