My "go to" puffy eye remedy is a 10 oz glass of warm or room temperature water first thing in the morning. If my eyes don't look less swollen in 30 minutes, I drink another one, but only 8 oz. It always works.
I have allergies and sinus issues that contribute to puffiness under my eyes. Aside from treating the allergies (which is important! ), I find aloe gel decreases the puffiness under my eyes. It also tightens my skin, makes it more radiant, and decreases wrinkles, so I use it twice a day on my entire face. I use only the brands sold at health food stores, not the kind you would get at a drugstore. There is a big difference!
I use fresh aloe on my eyes when they are tired and also all over my face (facial massage time!). I am amazed at how fast it works to reduce swelling and bags. I wash it off after about 20 minutes. I follow up by spritzing my face with mineral water. It's so dry here in AZ, especially in the summer. Interestingly, when I don't wash it off sometimes I end up with body odor that smells like the bitter component of aloe. I will try your suggestion of frozen and see if that works better.
I have been oil pulling for a few months and the dark rings have not reduced. However, taking iodine has taken the puffiness out.