With cellulitis (child), how long after oral antibiotx start should we see less symptoms? (swelling, redness, warmth in arm) (bactrim)

24-48 hours. It takes some time for the meds to work. Initially, antibiotics first stop the spread of infection before symptoms abate.
Only days. If a child has a suspected MRSA infection being treated with Bactrim (sulfamethoxazole and trimethoprim) i would expect improvement in 24-48 and be re-evaluated with any rapid worsening. Regardless follow should probably occur within 3-4 days maximum.