I'm pretty sure that sunbruno is actually suntan and sunbrulo is sunburn.
Bruli is intransitive. I think brulo here must refer to the sensation of burning:
Mi sunbrulas. I am sunburnt. (That is, "I am burning on account of the sun.")
Mi sunbruliĝas. I am getting sunburnt.
Mi havas sunbrulon. I have sunburn.
And it would work the same way for sunbruno.
More generally, a burn is a brulvundo ("burn wound").
Sunbruliĝo is "solar combustion", and is awkward to justify here (unless the metaphor is that your skin has "caught fire").