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We perform a sub-threshold follow-up search for continuous nearly-monochromatic gravitational waves from the central compact objects associated with the supernova remnants Vela Jr., Cassiopeia A, and SNR G347.3$-$0.5. Across the three targets, we investigate the most promising ~ 10,000 combinations of gravitational wave frequency and frequency derivative values, based on the results from an Einstein@Home search of the LIGO O1 observing run data, dedicated to these objects. The selection threshold is set so that a signal could be confirmed using the newly released O2 run LIGO data. In order to achieve best sensitivity we perform two separate follow-up searches, on two distinct stretches of the O2 data. Only one candidate survives the first O2 follow-up investigation, associated with the central compact object in SNR G347.3-0.5, but it is not conclusively confirmed. In order to assess a possible astrophysical origin we use archival X-ray observations and search for amplitude modulations of a pulsed signal at the putative rotation frequency of the neutron star and its harmonics. This is the first extensive electromagnetic follow-up of a continuous gravitational wave candidate performed to date. No significant associated signal is identified. New X-ray observations contemporaneous with the LIGO O3 run will enable a more sensitive search for an electromagnetic counterpart. A focused gravitational wave search in O3 data based on the parameters provided here should be easily able to shed light on the nature of this outlier. Noise investigations on the LIGO instruments could also reveal the presence of a coherent contamination.