It's always scary to have an abnormal Pap smear, but it's not really too big a deal.
HPV is a common virus that most sexually active people will have sometime during their lives. Most of the time our bodies get rid of it in 1-2 years.
The borderline changes are the very first step toward cancer, but often go away on their own, and do not suggest cancer at this time. If the changes don't disappear without treatment, they are easily treatable in the office.
The colposcopy is done to evaluate how significant the changes are, since the Pap smear only suggests what changes may be there.
If the changes are significant, then they can be treated, and they'll be gone.
I doubt that it would be worth going private. These are simple changes that are easy to evaluate and to treat.
Most of the time, HPV and borderline changes on a Pap smear are inconveniences and nothing to worry about. As long as you have follow up as needed, it will never be anything serious.