I had something similar, from triceps work and lat pulldowns with a certain type of bar. What i had is called golfer's elbow-same thing but on the inside part of the elbow rather than on the outside elbow area like tennis eblow. I scheduled a shot but then was able to avoid getting any treatment by the following changes, below. All the painkillers will help, but the problem is related to repetitive use that causes aggrevation, and will return unless the problem is dealt with by making some changes.
The type of grip used in any exercise makes a significant difference, both in terms of hitting the muscle differently and how and where the stress hits the elbows and other joints.
On skulls after taking a break until the elbow's better, take a longer warmup, do a triceps compound first for further warmup then for a few workouts each try one of several bars-triceps hammer grip, E-Z curl, super E-Z curl, two hands around the end of one dumbbell. Each will hit the joints differently.
And of course on "skulls" do the far better version triceps extensions in which the weight is lowered behind and well below the end of the bench. All the way down towards the floor, something like doing pullovers but with an extension motion, for a full stretch. Don't worry about elbow positioning. Skulls with the weight lowered to the face aren't as effective and are harder on the elbows IMO.
