She looked at me with tears streaming down her cheeks.

Literal

She [topic-は] cheeks [on-に] tears [object-を] flowing [while-ながら] me [object-を] looked.

~ながら chains two simultaneous actions performed by the same subject: 'while doing X, [she] also Y-ed.' Here the subject is doing two things at once — crying and looking. 涙を流す ('to shed tears,' literally 'flow tears') is the standard idiom; English would say 'tears were running down her cheeks,' framing the tears as the subject, but Japanese keeps her as the agent. ほほ (cheek) is also written 頬 — both are correct, though hiragana adds a softer tone. The に marks the cheeks as the surface on which the tears flow.