Yes, it is normal to have the swollen eyes after using anesthesia because of the stimulating irritates inner anesthesia. It will be temporary. You could use the warm compress to make your swollen eyes release to some degree. You should eat more food with vitamin C to keep your eyes moisture. At the same time, you should have the good rest for the eyes.
Yes, it is possible to have swollen eyes after anesthesia. I saw many people complained about this symptoms on internet. Some people even have swollen lips as well. Anesthesia originally come from Greek, which means having sensation blocked to temporarily taken away. It works by some certain single drug or a combination of drugs, such as analgesics, hypnotics, sedatives and so on to allow people undergo surgery. Actually many people experienced side effects from anesthesia. Some claimed dehydrated, nauseous, vomitting, headaches and pain in joints and muscles, sore throat, or swollen eyes. All of these side effects appear a few hours after the surgery, but in most cases these are just temporary symptoms and will clear out by themselves. Most symptoms are similar to a cold or flu. Some people get swollen eyes or lips, due to allergy reaction to the tap used. It is a possibility too. To lower the risk of anesthesia, you need to communicate with your surgeon as well as anesthetist, have them in the loop of your medical history and any reaction to anesthesua of your family.
As you can see, anesthesia or other drugs are somehow to some extent poisonous, which would give rise to some negative consequences to your eye health or other parts of your body. And if your eyes are allergic to such drug, you are very likely to have swollen eyes, but that is just temporary, what you should do is to rest your eyes and have a healthy diet, or just get some medical treatment.