Liz Buchanan BVSc MRCVS
Hi- thankyou for your message and pictures. It's no problem; it can be hard to upload things but I can see both from here. As well as the lump, I appear to be seeing a certain amount of baldness spreading around the eye; has the hair been cut to see the lump better, or is this another symptoms in your pup? Of course, this may be an effect of allergy, especially if it is itchy and being rubbed. But I wonder whether another differential might be a manifestation of either an autoimmune disease, or of demodex, a little mite that lives in hair follicles - which might also be responsible for such a lump.
Allergy, demodex and auto-immune disease are none of them usually treated with cold compresses, although bruising, as first observed / reported to your vet, would be. It sounds as though it's a good idea to have your vet examine this eye and see whether they can start to narrow down the causes, in order to assess, identify and treat the problem.