Everyone seems to be focused on the sting. My concern (as you can see what I bolded and underlined in my first response) is the rapid swelling of the entire arm from wrist to shoulder. My guess is that there was also erythema and edema involved too. It could be cellulitis, but it can also be necrotising fasciitis, osteomyelitis, septic joint, etc. with the sting being the point of entry (hence why my low threshold for surgical consult). The choice of antibiotics probably wasn't made at a whim (especially if the child was in the pediatric ICU). Several posters have suggested steroids and antihistamines - but unless you are certain it isn't anything that is potentially life or limb threatening, you treat under the assumption that it is a potentially serious infection.
And I've seen MDR organisms in kids. They are not limited to elderly nursing home patients with multiple admissions. Believe it or not, kids do get exposed to all type of bugs from all type of sources (kids do visit sick grandparents in hospitals/nuring homes, or have a sick sibling that requires frequent hospitalizations, etc). I've seen MDR-TB, ESBL Klebsiella, MRSA, resistent strep pneumo, etc in kids. Heck, I've seen NICU babies who after a few days would have positive MRSA swabs (either from family members visiting/touching, or healthcare workers) Don't rule out resistant organisms just because the patient is a kid.
It appears this kid was in the pediatric ICU. It also appears that mom is an extremely poor historian. Most PICUs usually have good social workers and care coordinators. A lot of PICU also have a dedicated Peds ICU Pharmacist as part of the team. I wonder if in this case linezolid was already prior auth and a pharmacy was already picked (such as the hospital's outpatient pharmacy) and the mom just didn't understand (or ignored what she was told) and went to her default pharmacy to get the meds?
We don't know what this child had (however it was bad enough to require a peds ICU stay).