Pretty much the only time you're ok to not use protection is if you're really ready to become pregnant or possibly catch an STD.
Protection really is a must. Methods like fertility awareness require time, and really aren't very practical or even very accurate in teens. Especially as a teen, you can potentially ovulate on any day of your cycle since it's still regulating itself. And sperm can live in a hospitable enviornment (your vagina) for up to 7 days. Even being on your period doesn't mean that you don't have a pregnancy risk. And that's not even mentioning your STD risk. Even if you think you and your partner(s) are clean, you can't be sure, since there are STD/STIs that can be transmitted by non-sexual methods. If you've been in a monagamous relationship (meaning no sexual contact at all with anyone other than your partner, not even open mouthed kissing, etc.) where you have been using protection everytime and you both have had two clean STD screens (every 6 months), then that's about as low risk as you're going to get as far as STDs go, and that's not promising that you won't catch something...cause you still potentially could.
So no, there's no really safe time when you can go without protection and not have a risk. Condoms are your friends.
There's hair there for a reason!
"Never insult an alligator until after you've crossed the river." ~Oriental Proverb