Do lip fillers like Juvederm increase gap between nose and mouth?

Usually lip fillers will decrease the gap. You may have some swelling, which can last up to 2 weeks. If after 2 weeks, you don't like your results, you can have the filler dissolved with hyaluronidase. Hope this helps.

The reaction you are describing is the opposite of what is typically seen.  It may be due to swelling, so I recommend waiting a full two weeks from the time of injection for the swelling to subside.  If you still have concerns at that time, return to your injector for an evaluation.

Lip augmentation typically decreases the gap between the nose and the upper lip. I think you should look at your before and after photographs for comparison. Good luck from New York City

Typically lip augmentation with fillers can be used to decrease the gap between the tip of the nose and the lip and it would be very unusual for you to notice the opposite result (based on your question). You should wait at least 1 week post treatment to determine if such "gap" is truly real. In the future if you still have such a concern, additional Juvederm filler can be injected right in the upper cutaneous lip (lip area above the red of your lip) to shorten such a gap. 

Lip filler shouldn't increase the space between your lips and nose. Sometimes changing a feature on your face makes spaces appear differently. This could be the case (but not necessarily a bad thing). If you are unhappy with your filler, you can always have it reversed with hyaluronidase. Best of luck!