A tiny bump near your eyebrow is probably a cyst or a skin tag, which are common and not usually a concern. They can form from a clogged oil gland or a blocked hair follicle. If it’s not bothering you, it’s okay to leave it alone. However, if it grows bigger, changes color, or starts hurting, it’s best to have it checked out.

Your rabies vaccine was completed last May, so you’re protected from getting infected by it. However, if a cat bit you today, watch out for any fever, headache or weakness that is abnormal. Seek medical attention immediately should you see any of these symptoms. 

Acne and pimple­s are skin problems many people­ deal with. Sometimes, afte­r acne clears up, dark spots remain. The­se spots are called post-inflammatory hype­rpigmentation. They happen whe­n your skin produces too much melanin due to inflammation. To he­lp reduce these­ spots, keep your skin clean and avoid picking or sque­ezing pimples. Using products with retinoids, vitamin C, or hydroquinone­ may gradually lighten the spots. Wear sunscre­en to prevent the­ spots from darkening further. 

From what you are telling me, a cat must have bitten you. And even though it didn't bleed, you saw a burning sensation and a red dot after the event. This is a possible result of bacteria from the cat's mouth. It is important to wash the area with soap and water. Check for any swelling, pain, or redness. If you see anything out of the ordinary, don't hesitate to see a doctor.

Yes, cysts and papules can be treated with various treatments such as  antibiotics, topical creams, laser treatments and surgery.  I advise you to consult a qualified doctor. Based on proper assessment of your problem, he may be able to suggest the most appropriate treatment for your pimples.