I suspect that the majority of teens deal with self-esteem issues, whether or not they have a strong and supportive family like yours. The teen years are a time of emotional and social uncertainty. You are figuring out who you are and who you want to be. Friends often seem fickle because they are also figuring out who they want to be and how to be with other people.
You have changed schools twice. In each place, the kids have already made their “friend group” where they feel safe. It probably isn’t personal that they aren’t incorporating you. I’m worried about the friend who seemed to drop out of sight. That may have nothing to do with you. She may have big troubles of her own.
The “cure” for your loneliness is to stop obsessing about it and to start doing things about it. Join school clubs or teams that interest you. Volunteer for some community service work that other teens are doing. When people do things together, they become more interested in each other and more bonded.
Don’t keep score about who is doing the inviting. If you want to spend time with people, invite them to do things with you — like going to a movie or school event. If you want them to celebrate your culture, consider asking your folks if you can invite some people you like over to your house for a real South of the Border dinner.
Self-esteem grows by doing, not by thinking. Get doing and you will develop that higher self-esteem you long for.
I wish you well.