After 3 days on the antibiotic she should be feeling better. If not, I would make a follow up appt with her doctor. She probably needs a different antibiotic. Another common treatment for lung infections is an albuterol nebulizer treatment and using a albuterol inhaler for a few days at home. This opens up the airways and helps make it easier for the person to cough up mucus.
Also, did she have a chest x-ray? This is important diagnostic test to see what kind of infection she has.
Hope she feels better soon.
that temperature itself is not a medical emergency. check her pulse and blood pressure.
when you say no other symptoms do you refer to any symptoms at all or just the ones you think that might be related to an infection?
what type of blood tests did she have last time and which values were out of range if there were any?
It will be difficult to have her hospitalized with just a mild fever. if it's not a medical emergency it would be a better choice to get an appointment soon with a specialist, even privately.