I am sorry to hear about this concern.
Do not squeeze any further, because it will contribute to inflammation.
Unfortunately, at this point, we really don't know if this is a nodule, cyst, sebaceous grwoth, or possibly a malig***** *****ke a mast cell tumor. I would leave it alone. As soon as possible, have the vet get a look at it, feel it, and than make a judgement call if a basic fine needle aspirate test needs to be done.Fine-needle aspirate test is performed usually without anesthesia and is very quick. Your veterinarian takes a few needle samples from the lump (the needle is no larger than the needle used to give vaccines). The sample is smeared on to microscope slides and submitted to the laboratory. It is not always as definitive as a biopsy (this is a full tissue sample), but often it can yield enough information to help guide you and your vet as to whether a biopsy is needed, or if surgery should be performed.
Hope that information helps
Putting some basic neosporin on it would be okay. If a little inflamed, some topical hydrocortisone cream is also suitable.
I would have it evaluated a bit sooner. When you squeezed it and it opened up, that could predispose it to getting infected.
Make sure to note for the visit what the fluid looked like that came out. That information might help vet a bit.
Sounds like a plan.
Might just be a cyst, insect bite/sting rxn, impacted hair follicle. Could be lots of things.