Hello Salome, Greetings from Prescott, and Welcome to the Forum!
Can you post a picture of the entire tree? Those spots look like they might be some sort of canker, sooty mold, or possibly nothing significant.
https://ipm.ucanr.edu/PMG/GARD...
It is unusual for plant diseases to be transmitted to humans. I'd be more worried about the tree falling on the house.
Are you concerned about coccidioidomycosis--Valley Fever? It is pretty much universally present in the soil in your area. It does not come from plants. It is common in humans, dogs, livestock, zoo animals among others. It is only transmitted by a fungus in the soil, not from others with active disease, and not from plants.
