All my partner wants is sex, and I consider myself a little too young. How can I tell them that I don't want to have sex without embarrassing them and hurting the relationship?

It’s nice that you want to spare your partner’s feelings, but it’s also your feelings that matter in this situation. People have a right to set boundaries in their relationships and to have those boundaries respected. Being straightforward and honest about those boundaries is an example of healthy communication.
Let your partner know that you’re not out to embarrass or hurt them, you just want to open up the lines of communication regarding a boundary that you have. Remember that you can’t control their reaction, but your boundaries are still important and should be respected. Explain to them why you feel that having sex isn’t the best option for you. A partner who cares about and respects you won’t pressure you to have sex before you’re ready.
As far as your relationship goes, not having sex doesn’t mean you want to end the relationship. Be clear about this if you want to stay in the relationship. If you two are together because you really like and care for each other, then letting your partner know how you feel may help to bring you closer. . There are a lot of ways to feel close to a partner besides having sex, and they’re not all physical. This could be a great time to talk with your partner about what you are comfortable doing that would help you feel closer to your partner.