Do a malware check with a few malware scan programs.
You need to use all programs because each detects different malware.
Make sure that you update each program to get the latest version of the database.

• http://www.malwarebytes.org/mbam.php - Malwarebytes' Anti-Malware
• http://www.superantispyware.com/ - SuperAntispyware
• http://www.safer-networking.org/en/index.html - Spybot Search & Destroy
• http://www.lavasoft.com/products/ad_aware_free.php - Ad-Aware Free
• http://www.microsoft.com/windows/products/winfamily/defender/default.mspx - Windows Defender: Home Page

See also "Spyware on Windows": http://kb.mozillazine.org/Popups_not_blocked and What to do when searches take you to the wrong search website

Thank you but I first want to understand if cookies left on my computer from a porn site effects my search results in the future?

It is usually best to let all cookies expire if you close Firefox and make an exception for the ones that you want to keep. Cookies only have effect if you (re)visit a website from which you have cookies saved from a visit in the past.

See Cookies - Information that websites store on your computer and Enhanced Tracking Protection in Firefox for desktop

There is usually no need to enable third-party cookies.