Sp taking a quick glance at your profile doesnt show any red flags on your account being used to boost/sharing account. But seeing how your account was flag as using a 3rd party program, you have to remember that it also takes into account what is actually being used with the programs for League of Legends. What kind of stuff do you have on your computer that might being also used in league of legends that isnt obvious. EG: things like Discord/Razer/Skype/overwolf(?) wouldnt trigger the 3rd party program finder as those are "ok".
But there are some programs that even if you dont use it will still trigger it if they find it on your computer! Try to see if there is anything you dont know about on your computer. Does other people use the computer that might have downloaded stuff?
The only other option you have is to contact Support and let them check again. It would help if you give them details on what is on your computer as they might have stuff that isnt updated on their system that could trigger the detection!