In an animal airway model, name an exogenously applied agent that will
produce both an acute bronchoconstriction AND an inflammatory cellular
influx

Inhalation of aerosolized ovalbumin will cause both these reactions to
occur in animals such as rats, mice and guinea-pigs which have
previously been sensitized by intraperitoneal or intradermal
injections of ovalbumin.

For example:
Histopathological and immunohistochemical studies on experimental
asthmatic model induced by aerosolized ovalbumin inhalation in guinea
pigs.
Sato Y, Kishi T, Umemura T.
Research Center, Kyorin Pharmaceutical Co., Ltd., Tochigi, Japan.
Journal of Toxicological Science 1998 February; Vol 23(1):69-75

"To establish an animal model of asthma, fully sensitized guinea pigs
inhaled aerosolized ovalbumin after booster treatments... From 1 to 6
hours after provocation, anaphylactic changes such as perivascular
edema and bronchoconstriction were detected. After that, intensive
infiltration of eosinophils appeared and lasted until 48 hours after
provocation. "

Search strategy: I was already familiar with ovalbumin-based asthma
models, so I searched on the terms: ovalbumin, asthma,
bronchoconstriction, infiltration