It looks like this isn't resolved yet. If I were you, I would:
1. Log into your account, and take a screenshot inside your NetworkSolutions account showing that the domain is there.
2. Take screenshots of the Whois page at
https://whois.icann.org/en, and the Whois page at Network Solutions (where your contact info isn't showing), and also the Whois at Godaddy for your domain.
3. Write an email to NetworkSolutions about the problem; be polite and point out the error. Request that it be corrected as soon as possible. Attach all the screenshots.
4. Also get on the phone to NetSol and tell them of the problem, saying you're sending them an email outlining it all, ask for help, and get the person's name you speak to. Write the name down with the time/date you talked to him or her.
That should cover all bases. You've preserved information visible online, and gotten the problem on the record with your registrar by emailing. Keep contacting them if they don't solve it right away. I don't see why they can't, actually.
Your own registrar is the one you should be able to expect an accurate Whois page from. Other Whois services may lag behind.