Keep a simple record: the date, room, surface and what you noticed. Take a photo from a safe position if practical. Include nearby context, but do not pick up droppings, scatter them or collect them in your bare hands just to make an identification photo.
If rodents may be involved, do not dry sweep or vacuum droppings, urine or nesting material. CDC explains that disturbing rodent waste this way can put contaminated particles into the air. Follow its current cleanup guidance or ask the appropriate professional or local health department about your situation. Do not mix cleaning products or improvise a pesticide recipe.
EPA notes that cockroach waste and body parts can trigger asthma in some people. This guide cannot assess personal health risk or diagnose symptoms. For health concerns, speak with a healthcare professional; pest identification and medical advice are different tasks.
Use CDC guidance for possible rodent waste; see EPA information about pests and asthma triggers for general health context.