When I had the problem of getting an internal exam, my doctor gave me a choice (I was 17-18 at the time) 1. since I was in a relationship I could have an internal now 2. since I was in a relationship I could wait until I was 21 BUT I had to take the gardisil shots to vaccinate against HPV (a cause of cervical cancer). As an asexual I wasn't exactly happy about getting an internal, BUT it's an important part of making sure your body is healthy.
It is, particularly if you are sexually active or at high risk of cancer/other problems. However, your mental health is just as important as your physical health. Why am I emphasizing this? Because if having a gynecological exam causes panic or other severe emotional distress, it is not worth it. You do not have to sacrifice one form of health to check another. If everything seems to be a-ok with your vagina/uterus/etc, and having an exam would be panic inducing, it is okay not to. You always have that option - it is your body and you get to say what happens to it.
Like Di, I have never had a gynecological exam. I am 23, I am not sexually active, I have no symptoms of any problems whatsoever. I am low risk. I am also not comfortable (but not necessarily panicky) about people getting up in my business, and specifically, I cannot do anything penetrative. Not even tampons. Very painful. So, knowing most of what a gynecological exam entails, knowing that part of it is a speculum exam (inserting a device into the vagina that opens it up and allows the doctor to examine the inside/take swabs), I know that it's not even an option for me. So, I continue to decline to have said exam when I visit my doctor. Even though I know preventative care is the best care and it's a good idea to get checked out, I continue to say no.