I'm not sure what medication you're taking, but I encourage you to tell your doctor about the side effects you are experiencing. It may be nothing, or it may be a sign that it is not the right med or dose for you.
I've been on SSRI's for years (I think 16 or 17 years now - first Prozac and now Paxil). I've had various side effects but they usually go away within the first few months. The most notable I recall were sweating more, dry mouth and decreased libido.
I'm sorry to hear it's difficult for you to talk to your parents about your anxiety. I have had similar experiences.
My mom, while very loving, is a bit dismissive about any sort of mental health "stuff". I think that is just the way she was raised. Plus, she is so calm I sometimes wonder if she even has a pulse. I just remind myself that a) she loves me and b) while she's not the number one person I can talk to about my anxiety, she does care about me and wants to know if I am struggling or if I am ok in general. So I keep it general with her.
My dad also had anxiety (and his father before him). I couldn't talk to him about it at all, we just didn't have that type of relationship. It was just one of those things that I had to grow to accept. Again, I knew he loved me, but I saved my detailed conversations about anxiety for my therapist, sister and close friends. It wasn't perfect, but it was what I had. I talked to him about other things.
I'm not sure if you are in therapy at the moment, but that has really helped me. They HAVE to listen! Also, I have joined a Meetup.com group in my area for people with anxiety and depression. That group has been really helpful. Just getting it out, talking to someone who KNOWS exactly what I'm talking about is so nice.
Best of luck to you.