Is it safe for a patient with leukaemia be given tobramycin, even if they get an infection?

Yes: Tobramycin might be given to leukemic patients with chemotherapy induced lack of white blood cells and fever. It is only used if a patient is felt to have an inf. Other antibiotics are usually used in this situation as they are less likely to be toxic to the kidneys than tobramycin. For pseudomonas infection in a leukemic patient tobramycin would frequently be used along with another antibiotic.

Eye drop blood effec: Not likely going to be a concern in ointment for the eye infections. Drops can track through to the nose when instilled in the eye and thus give exposure to the lekic but short. Course usually required of eye infections not likely a problem. Punctual occlusion after drop placement can also help reduce systemic exposure.