Epiglottitis, pneumonia go together?

Not exactly. They are infections in 2 different places, pneumonia being an infection of the lungs and epiglottitis is and infection of the upper airway (particularly the tissue that close off the wind pipe during swallowing to prevent aspiration). One of the bacteria that commonly causes epiglottis can also cause pneumonia (hemophillis influenza), could occur together but not usually.
Different diseases. Epiglottitis is usually (but not always) a childhood illness, generally caused by hemophilus influenzae, which can be life-threatening and is an infectious disease emergency. It could conceivably lead to pneumonia, but the latter is a disease of lung tissue which occurs regularly in the absence of epiglottal infection.
Can be together. 25% incidence of both pneumonia and cervical lymphadenitis was found to be associated with epiglottits in one series. Exudative tonsillitis and otitis media were the only other complications, although they were infrequently noted.