...but the thing is he was more "toxic" than I...
Them being more toxic than you doesn't change that you both broke the rules.
...and would like to see the whole game chat logs to make sure he was 100% more verbal abusive than I...
It wouldn't matter if he was. You'd still be punished, because you broke the rules. Doesn't matter if someone broke the rules in a worse way than you - you still broke them.
...and how he made up lies for the enemy team to report me and how his duo and some other kid on my team ganged up on me to report me.
If he was lying about it, let him lie. False reports don't do anything.
If he was in a duo queue, then guess what? That doesn't change anything. The IFS doesn't care how many reports are filed, only that there's at least one. You got punished because the subsequent review found your behavior below the acceptable standard, not because you got ganged up on and reported by a bunch of people.
So over all is it possible to get the chat logs of the whole game for my team or do i have to deal with this BS?
Technically, yes, it is possible, as Riot does have access to the full game chat logs, but while it is possible, it's wholly unnecessary. You alone chose to type what you did to merit the punishment, and Riot won't overturn the punishment just because someone else said worse than you.
Next time, if someone starts lying about you, mute them, and don't say anything to them or about them. Let them lie, and watch as their report does nothing because you didn't break the rules.