Keep in mind that there are many reasons your ping could be going up during a game:
-Your ISP throttles high packet numbers such as online gaming (more likely if you use a cellular/4G/similar internet, but possible with other internet plans)
-Your ISP experiences high numbers of connections to Riot's servers (possible if you play at a university/on the same "pipes") and is overwhelmed due to not having enough bandwidth between them and Riot. I know Riot and other major companies try to have "direct links" (in simple terms) with many ISPs, and it's possible yours doesn't have one or it's malfunctioning/not working.
-Your router struggles with the high number of packets, causing packet loss. Probably only with an extremely old router.
-You may have a virus or some sort that operates when intensive processes (such as videogames) or other things League triggers are happening.
-Riot's servers may just be having issues.
I'd suggest submitting things such as your nettrace and other logs suggested HERE to Riot at https://support.riotgames.com and see if they can help you identify any problems - they're more experienced than me for sure.