Honor is not going up

You will just have to keep on playing clean games. There's really not that much else to it.

It might take some time until you unlock your honor level but eventually you will be eligible to once again rise in Honor levels.

If you find yourself getting frustrated easily and voicing that via the in-game chat using the /mute all command is definitely a good idea (all relevant communication can be done through pings).

Note that single reports won't really hurt your progress to getting your honor level unlocked again. Random players reporting people are unfortunately a thing but as long those reports remain an exception you shouldn't have any trouble.

Also: If you find yourself getting frustrated consider taking a break from the game for a moment to calm down. Everyone gets tilted from time to time but if you do realize it some distraction doesn't hurt.

Link to the Riot Games Honor FAQ:

PENALTIES AND LOCKS

How do I drop a level in Honor?

You’ll only drop if you receive a penalty. A chat restriction knocks your Honor level to 1, or 0 if you’re already at level 1. A two week suspension will drop your level to 0 (even if you were higher). In both cases, your honor progress will be locked, making your account ineligible for hextech crafting rewards. Your honor progress will unlock some time after your restriction as long as you show signs of reform.

What do you mean by lock my Honor level and rewards?

You'll see a lock on your Honor level in your profile. This means you aren't making any progress to the next level, and you won't receive any rewards. Unlock your Honor level by putting clean games in. You’ll get a notification when you’ve unlocked your Honor level.

What's the deal with level 1 and 0?

If you fall below level 2, you were hit with a penalty or two, and the first step is to put in clean games to unlock your Honor level. Once you do, your games help you climb back to better rewards, just like how it’s worked since Loot launched.

As someone with multiple accounts, I can tell from experience that Honor is time-gated and not as dependent on number of games as it is commonly believed to be.

Playing a number of games where you get commended / don't get reported over a huge amount of time (months) is more important than playing 80 games in a row without getting reported.

During testing, I found that it took me the same amount of time to get to Honor checkpoints regardless of whether I play 5 games or 30 games a week. These checkpoints seem to trigger around the same time every few weeks.

That said, if you want to rake in commendations as fast as possible, I'd recommend you play 3v3 bot games as the requirement for the bonus 'all players on your team have honored someone' is lower (3 players instead of 5) and average game length (8 min) is shorter.