I’m going to first advise you that if there’s truly a sudden onset of puffiness then you should rule-out anything related to the thyroid such as Graves' Disease or thyroid-eye disease, otherwise known as thyroid-related immune orbitopathy. Although you don’t have the classic appearance of someone with Graves' Disease, I advise you to see an endocrinologist and ophthalmologist to check for this sudden onset of swelling.
What you likely have is called lower eyelid fat prolapse. This means that the fat that’s normally behind your eyes pushes forward and creates a bulge known as herniated fat. Since it is a fat pocket pushing forward, it is impractical to consider any non-surgical options. As a specialist in cosmetic eyelid surgery, I routinely see patients who have tried every non-surgical, do-it-yourself, and over-the-counter product such as cucumbers, tea bags, hemorrhoid creams, and all kinds of topical treatments that don’t work. Also, a certain percentage of people will visit a non-surgical physician like a dermatologist or an aesthetic physician and get injectables. An example is called Restylane that camouflages the bag. In my experience, I see patients almost every week who come in to have those injectables dissolved. This is because when you have a volume of fat pushing forward and you try to add a volume of hyaluronic acid that attracts fluid to try to camouflage it, you get larger bags.
Based on your photos alone, I would suggest a surgical procedure called transconjunctival blepharoplasty. In this procedure, the fat pockets that have pushed forward can be reduced, sculpted and repositioned from the inside of the eyelid. By doing that, there is no scar and no one would be able to tell that you had surgery. In my 20 years of cosmetic surgery practice, I’ve dedicated myself in finding a quick recovery approach. Most of my patients actually get back to work in a few days or less than a week. For example, if somebody had a surgery on a Wednesday, they can go back to work on Monday. Although there is still a little bit of bruising and swelling under the eyes, patients can choose to apply moisturizer, foundation or even wear tinted glasses to camouflage the area.
We perform this procedure under local anesthesia with light IV sedation, and the procedure is usually done in less than an hour. I recommend finding a cosmetic surgeon who is in the oculofacial field because of the extensive experience in eyelid surgery, and someone familiar with people like you who need a quick recovery. I hope that was helpful, and thank you for your question.