As noted above: A 13-year-old needs parental/guardian permission to set up a publisher account. If the games cost money, that involves a bank account somewhere, which also means needing adult support.
Content restrictions for 13-year-olds are "whatever the law allows in your area." In the US, that's pretty broad as long as they're not dealing with photos of minors. (I don't just mean sexy photos; there are privacy laws involved.) If they stay away from sexual content, there may not be any limits.
But for the practical side of things: NEVER TELL ANYONE ONLINE YOU ARE UNDER 18. Because there are predators online who look for young people who don't know how to spot them. The predators are not the ones who will reply with "kids should not be making this kind of content" or "I guess it's okay if your parents agree." Predators will say "oh that's great - let me help you! I turned 18 two months ago and everyone was mean to me when I was thirteen; let me show you where you can host files that your parents can't find them; I'll help you set up a bank account - I'll be the co-signer and pretend to be your parent, okay? What's your address? Oh, and your birthday and social security number; we need those."
Make the content you want to make. As far as sharing it goes - Find a trusted adult who understands internet safety and talk to them about it. Not "someone who can lecture you about creepy predators" but "someone who knows how you can avoid doing something now, that you won't care about for several years but could mess up your chances to get into the college program you want." The dangers aren't limited to "some jerk tries to scam you or get creepy at you."
(Would a gore-fest video game mess up your college chances? I have no idea. I don't think so. But I'm long past caring what other people think of my hobbies - and am not in a position where people can use them against me.)
Will your high school teachers be able to find this post in three years? You don't know! Itch.io doesn't even know; they have no idea what forum software they'll be using in three years, or how searchable their old archives will be.
If you are going to a forum full of strangers to say "I'm 13; please help me figure out what to do" - the answer is going to be "talk to your parents, and please keep yourself hidden for another few years." Because you obviously don't know what the risks are, so you don't know how to keep yourself safe.