  The Rosette Nebula is an HII region ionized mainly by the stellar cluster NGC
2244. Elephant trunks, globules, and globulettes are seen at the interface
where the HII region and the surrounding molecular shell meet. We have observed
a field in the northwestern part of the Rosette Nebula where we study the small
globules protruding from the shell. Our aim is to measure their properties and
study their star formation history in continuation of our earlier study of the
features of the region. We imaged the region in broadband near-infrared (NIR)
JsHKs filters and narrowband H2 1-0 S(1), P$\beta$, and continuum filters using
the SOFI camera at the ESO/NTT. The imaging was used to study the stellar
population and surface brightness, create visual extinction maps, and locate
star formation. Mid-infrared (MIR) Spitzer IRAC and WISE and optical NOT images
were used to further study the star formation and the structure of the
globules. The NIR and MIR observations indicate an outflow, which is confirmed
with CO observations made with APEX. The globules have mean number densities of
~$4.6\times10^4 \rm cm^{-3}$. P$\beta$ is seen in absorption in the cores of
the globules where we measure visual extinctions of 11-16 mag. The shell and
the globules have bright rims in the observed bands. In the Ks band 20 to 40%
of the emission is due to fluorescent emission in the 2.12 $\mu$m H2 line
similar to the tiny dense globulettes we studied earlier in a nearby region. We
identify several stellar NIR excess candidates and four of them are also
detected in the Spitzer IRAC 8.0 $\mu$m image and studied further. We find an
outflow with a cavity wall bright in the 2.124 $\mu$m H2 line and at 8.0 $\mu$m
in one of the globules. The outflow originates from a Class I young stellar
object (YSO) embedded deep inside the globule. An H$\alpha$ image suggests the
YSO drives a possible parsec-scale outflow. (abridged)
