  Owing to their quiet evolutionary histories, nearby dwarf galaxies (stellar
masses $M_\star \lesssim 3 \times 10^9 M_\odot$) have the potential to teach us
about the mechanism(s) that 'seeded' the growth of supermassive black holes,
and also how the first stellar mass black holes formed and interacted with
their environments. Here, we present high spatial-resolution observations of
three dwarf galaxies in the X-ray (Chandra), the optical/near-infrared (Hubble
Space Telescope), and the radio (Karl G. Jansky Very Large Array). These three
galaxies were previously identified as hosting candidate active galactic nuclei
on the basis of lower resolution X-ray imaging. With our new observations, we
find that X-ray sources in two galaxies (SDSS J121326.01+543631.6 and SDSS
J122111.29+173819.1) are off nuclear and lack corresponding radio emission,
implying they are likely luminous X-ray binaries. The third galaxy (Mrk 1434)
contains two X-ray sources (each with $L_{\rm X} \approx 10^{40}$ erg s$^{-1}$)
separated by 2".8, has a low metallicity (12 + log (O/H) = 7.8), and emits
nebular \ion{He}{II} $\lambda$4686 line emission. The northern source has
spatially coincident point-like radio emission at 9.0 GHz and extended radio
emission at 5.5 GHz. We discuss X-ray binary interpretations (where an
ultraluminous X-ray source blows a 'radio bubble') and active galactic nucleus
interpretations (where a $\approx 4\times10^5 M_\odot$ black hole launches a
jet). In either case, we find that the \ion{He}{II} emission cannot be
photoionised by the X-ray source, unless the source was $\approx$30-90 times
more luminous several hundred years ago.
