You say ‘even after washing your face’, so I presume you wash your face with cold water and possibly a compress to try to reduce the puff.
But in case you mean it happens after washing your face, the following are worth considering as culprits:
If your skin is sensitive or you have suffered from any allergic reactions to cosmetic ingredients, this could be from a face-wash or soap. Face washes commonly contain: preservatives, colour, perfume, essential oils, foam-boosting surfactants and lanolin, from wool, all of which could cause your symptoms. Just check the packet/bottle to see if you have SLS or SLES in there; common but harsh surfactants. Most washes have an alkaline pH and if it is high, this can do it too. It could also be from your shampoo or conditioner if you take showers or shower them off, as it will run down your face and could be irritating.
If your eyes and lips are both puffy, and by puffy I am assuming swollen, finding the cause is easier when you know when this happens. If it is just in the morning, after waking, and it reduces throughout the day, that could be localised oedema (fluid retention)and there are a myriad possible causes: simply not sleeping enough; anaemia (iron or B12 deficiency); several underlying health conditions from simple to complex can do it; a family tendency, with no apparently condition or just when you get very hot, fluid can pool. Your age is a factor too. Any new makeup or skincare would make me suspicious that it could be contact dermatitis, if so, simply stop using them for a few days and see if it improves. If you drink alcohol, this can cause slight oedema under the eyes, and possibly lips too.
The more serious concerns, if it isn’t just something you have on waking, could be: allergies, to anything from pollen (is it worse in summer?), dust mites or animal fur, for instance. Angioedema is a condition that often affects the eyes and lips. This, again can be from an allergen listed or from certain medications (if you think this could be it, don’t suddenly stop the medication without discussing it with your prescribing doctor.)Too much salt in your diet can cause your body to hold on to fluid (fluid retention, similar to oedema), so that is worth watching. Sinusitis can make those little channels in the face swell and they can inflame and push up the soft tissue under the eye, not so much lips, but it’s possible, if it’s really clogged. The more worrying potential causes could be kidney infection or disease, thyroid disorders, diabetes or heart disease/ poor circulation - but I think you’d have other worrying symptoms that you would already be aware of, if any of these were the cause.
If nothing here seem to fit, I can only advise you use a cold compress - just cold water - and lie with it across your eyes and lips for a couple of minutes in the morning or whenever you notice it is worse. Cut down or stop, if you drink alcohol, reduce salt intake and try to get enough sleep that you feel properly rested. It can also improve if you sleep with your head elevated - so it is higher than your feet.
If it continues or you have other symptoms, it is worth booking an appointment with your GP or practice nurse. You can be throughly checked there and they will probably offer you good advice as to how it might be reduced, having examined the areas.
I hope you find some relief soon.