My lips have gone really swollen after filler. Is it suppose to swell this much? I'm really concerned. (photo)

Hi, swelling is a common side effect following the injection of fillers. Certain areas, such as the lips, are prone to a quite significant swelling, which is probably what you are experiencing. 
The swelling is usually at its peak on the day of the treatment and the day after the lips have been injected, and usually improves slowly over the next few days. However it can take up to two weeks for you to see the final result. A cold compress with ice packs helps the swelling come down more quickly. If it gets worse or becomes painful despite cold compress, you should see your doctor again, and he/she can advise if anything further needs to be done. Otherwise, in a few days, once the swelling has settled, I hope you will enjoy your new plumper lips. 

I dont use that product, but it is a hyaluronic acid and they can cause temporary extreme swelling for a day or two in about 1/10 people. 
If your lips looked good straight after, that is how big they will look without the swelling. 
Take an anti histamine, sleep on your back and use an icepack to settle this quicker.