I have just googled 'Omegle' - I had never heard of them - and the concensus is that the site itself is safe but it is possible to get infected through using it.
As a first step, I suggest you download, install and run both Malwarebytes and Super AntiSpyware which are free downloads you can get from the downloads section of BC.
When you install and run both of these anti-malware products, let them update themselves, then run a quick scan with both.
If either of them come up with any problems that they cannot fix themselves, then start a topic in the 'Am I infected?' section of BC. Give details of your computer, a description of your problem and say that you have run Malwarebytes and Super AntiSpyware. Be patient, the people in that section of BC are busy !
Some malware is capable of preventing you from running treatments like Malwarebytes. If you find that you cannot install Malwarebytes, then post immediately in the 'Am I infected?' section.
Edited by Chris Cosgrove, 17 May 2014 - 05:41 PM.