Headaches have different origins but one of the most common origins is from the base of the neck. The facets at C2-3 and C3-4 can cause irritation to the greater and lesser occipital nerves. These nerves innervate the base of the skull and back of the head.
Facet irritation generally does not show up on an MRI and has to be diagnosed by facet blocks (see website under this procedure).
In regard to the “disappearing disc bulge” at C4-5, it is possible that there were two separate radiologists with differing appreciation of disc wall abnormalities. One would call the bulge and one would ignore it.
Occasionally, if the scans were performed on two different MRI scanners, one machine might have better resolution than the other and reveal the bulge.
In general, these bulges do not “go away”.