Thanks very much for the info.
So it seems as if the only way I can make the info private is to pay for privacy. Great! 
They are asking for $5, but I can't find out if that is for a year, a month or other period. Any idea?
Chris.
I would image that it is per month which would be way too expensive. Five dollars a year would be much better and one of the better bargains.
Many good hosting services provide free domain privacy for WHOIS as part of the hosting package. Might take a read at Wikipedia: Domain privacy
Wikipedia gives information, but can be outdated sometimes. This seems to be a little more informative: Domain Privacy Protection: Is It Worth It?
Some paragraphs from the blog about the downsides:
1) "Your Information Might Still Be Public
Private domain registration can be set up at any time, but if your domain was already registered without privacy protection in place, your information might still be public. There are tools available that allow people to do historic searches and find previously listed ownership data on domains. Some of these tools may even show transfer or sales records of domains."
2) "Who Actually Owns the Domain
Whenever you opt for privacy or WHOIS masking, you should understand the implications of putting someone else’s information down as the registrar of the site. In the eyes of the registry (ICANN or CIRA), the individual or organization listed as the registrant for the domain is technically the legal owner of that domain name.
That means that even if you’ve paid for registration, you’re not the legal owner if your name is not listed in the WHOIS. Mind you, you aren’t likely to get into a legal battle with the registrar about who owns the domain. Still, if it were to ever come down to a legal dispute, the registrar could come out the winner with their information down as the site owner."
As I stated before, your WHOIS information has already been "out there" and making it private now may not be enough. You can still login to the Control Panel and change the phone number, but the hosting site may have already sold some of your information. Definitely it has been pulled from the WHOIS site.
You could switch to a more reputable "free" hosting site and transfer the files and domain name to them after you discuss setting up WHOIS privacy. The better hosting sites do offer free WHOIS privacy, but usually these require a paid hosting service.
If you need more help, you can send a private message to me on this site. Useful if you don't want information in the public forum.
I just shut down 3 sites for a lady in Alabama as she hates logging in and using the control panels. All of the sites, except 1, were free sites. She didn't want to pay extra for privacy protection, but has not received any phone calls like you have. Her sites have been up for a long time.
Is there anything I can do specifically for you?