Is love just caring about someone?

In a simplified way, sure. There are four possible states in a relationship. Only one is actually love.

Love is caring about another person enough to care for our own wellbeing as well as another person’s wellbeing. To be responsible for managing one’s own emotional states as well as another person’s emotional states. Being able to be vulnerable AND accept another's vulnerability at the same time. To make another persons life better and allow them to make yours better, too. Both working to build each other up. That’s a two-up situation. That's love.

If you care about another person more than you care about yourself, you're going to end up victimizing yourself and that's not sustainable. You're always in a one-down situation.

If you care about yourself more than you care about another person, the end result is that you end up victimizing someone else. That's not sustainable. You're always in a one-up situation.

If you don't care about yourself and you don't care about anybody else either then the destruction of the relationship is much faster. This one is actually toxic because you're always in a two-down situation.