How do I keep caring without burning out?

You have learned the thing that saves people in caring work: you cannot pour from an empty vessel, so you tend the vessel. That is not a lesser kind of compassion. It is the only kind that lasts. Plenty of good-hearted people burn out because no one taught them what you now know. The key is that caring is renewable, but only if you actually renew it. Rest, boundaries, and things that fill you back up are not rewards for after the work. They are part of the work, the maintenance that keeps you able to show up tomorrow and the year after. So keep the practice honest. Check your own levels the way you would check on anyone you care for. When you notice the well getting low, refill it before it runs dry, not after. You have found a sustainable way to care. Protect it, and you will still be giving long after others have quietly gone empty.