I’ve had my first Juvederm lip filler’s today, feeling very uncomfortable afterward -- is this normal?

Yes, this can be typical. Icing and cold compresses can give improvement. It can take 1-2 weeks for final results. I would wait a full 2 weeks before judging the results. If it is after the two week wait, you can have the filler reversed with hyaluronidase.
I hope this helps!

Thank you for your question. 
What you are experiencing is absolutely normal. Swelling, tenderness can last several days to a week. 
The difficulty in eating and drinking could be from the swelling and the local Anestesia in the product. Ice and elevation are your  best choice 
If these symptoms persist beyond one week Please consult your surgeon injector or a local board certified facial plastic surgeon for more information and a comprehensive consultation 

It is common to feel a little sore after the lip injections as there can be bruising and swelling of the lips.  This generally will resolve by two weeks.  In the meantime you can gently massage the area and use ice intermittently the first couple of days.  Taking an over the counter pain medication such as acetaminophen may help with the discomfort as well.