Now don't take this the wrong way, I don't mean to insult you or offend you in any way shape or form. And this is coming from a girl's perspective.
Now I'll give you advice and hit some points. If your team is flaming you, mute them. Don't fight back. If you want to defend yourself, that's fine, but you have to know that you shouldn't offend anyone while doing so. In my opinion, staying quiet seems better than fighting back since you may or may not receive a chat restriction or a ban. Of course, you wouldn't want to be banned or restricted, would you? Just mute, report, and move on like Telephone Booth said. And as well as Autumn Rain, people are going to need to vent when they are angry. Some are immature enough to do it while in game. So if you see anyone flaming, either at you or someone else, just mute and report. And besides, there only needs to be one report to flag the game, not nine.
Now about you being sarcastic. We know you love to do it, and I understand that it may be fun for you. But in my opinion, sarcasm is still toxic. For example, your support goes out of lane to ward and he/she gets killed by the enemy jungler. Suddenly this pops up in chat. "Gee, Soraka, that was really nice of you to ward river without me." What do you classify that as? Excellent behavior? That is still toxic. Besides, what if you're the support? If the person was sarcastic towards you, would you like that? Of all my times supporting and having a really sarcastic ADC, it was torture being stuck in a game with them. Would I like it? No. No one likes it and you need to learn to not be sarcastic. If you continue to be sarcastic, then you are just lowering yourself to everyone who's toxic's level. You will be described as toxic if you mean to be sarcastic or not, so it's better to not even try to be sarcastic.
And about gender equality. If you use your period as an excuse to be toxic, that is not gender equality. And if you have trouble keeping your emotions in hand while on your period, and I don't mean to be insulting or offending, then don't play at all and try something else. If I had you in my game and you're being toxic, I'm just going to report you anyway. If you submit a support ticket about your report. What's Riot going to say? They wouldn't care since your behavior was out of hand. It would be the same for a guy as well. If he was toxic, he would be reported. He would be reported as well if males had periods and he couldn't keep his emotions in hand. It doesn't matter. On League, gender doesn't matter. If you were toxic, you will be reported and banned. If you were positive, you would receive the same honors and rewards as anyone else. If you don't do anything, then you don't get anything if you were either a boy or a girl! Mentioning "Guys will generally be nice to females but they should be to males as well. I am a female though but what's it them if I play a male champ or not" is just ridiculous. Men won't be nice to me. I would still be flamed if I did something wrong. If I just blatantly tell them that I'm a girl, they wouldn't be all, "Oh I'm sorry. I won't flame you." They would just keep flaming me regardless. And my boyfriend too. He gets flamed whenever he makes a bad play. If he says "Hey I'm a dude too! Don't flame me!" The other guy would just keep flaming him regardless if he was a boy or a girl. Like I said, gender equality doesn't matter in League, or any other video game. What does matter is behavior. Now is that too hard to understand?