This is "normal" in that it can happen, and it does improve. You might massage the area gently and slowly in a and continuous outward motion from the skin next to your right side of your nose to the right side of your face, making sure to apply something slippery first like Aquaphor, to push some of the accumulated fluid out of the area. You should try to drink lots of water and reduce salt in your diet. Elevate your head with pillows and lie on your left side or back when sleeping. Applying cold compresses and a properly formulated green tea cream such as Replenix (a substitute is a moistened tea bag that has been frozen) can help a lot. If you squint your eyes tightly shut repeatedly, the periorbital sling of muscle around the eye will squeeze away some of the accumulated fluid.
I have good success in avoiding this problem by performing a "snap test" before injecting under the eyes, and being cautious about injecting anyone with a history of puffy eyes in the morning that improves during the day, or a history of lower eyelid surgery. These patients can have compromised lymphatic drainage from their lower eyelids, making it difficult to eliminate the fluid that is attracted to some types of fillers. I also limit the amount of filler I inject in this area in one session, very rarely exceeding one syringe. Beletero is the least likely to attract water of all the hyaluronic fillers used in this area.
Swelling to the under high areas after any type of filler is a common issue to have. The swelling will always be more pronounced in the first week following the injection. However, the swelling will sometimes remain based on the location the filler was placed, or the individual to receive the injection. Cold compresses, gentle massage, and patience, are all part of managing this complication when it occurs. If the swelling persists however, dissolving the filler with hyaluronidase may be the best option. After one week to two weeks of observation, it is a good time to have a discussion with your provider.
Belotero or any under eye injection with filler can give you bruising or swelling. Since it has only been five days I would wait up to two weeks. If after two weeks you are still swollen I would return to your treating physician for evaluation. It is always important to find a board certified dermatologist with a great deal of experience with cosmetic dermatology and injections for the best results.