Why Does my Nose Feel Hard After Juvederm Injections in It?

You didn't mention where on the nose you were treated.  If it was used to volumize the tip of the nose, you could easily feel residual distention even 5 months later.  Studies have shown long term collagen stimulation in areas of hyaluronic injections even after a year or more but this should not really feel any different than normal skin at a later date.  What is reassuring that after hyaluronic injections the skin ultimately will return to baseline normal in time assuming no further product is injected. 

        Juvederm, depending upon the volumetric amount injected, may have given a tightening effect to the skin envelope.  In addition, there is some subtle scarring that can occur with any injection.

Juvederm is soft but it expands and fills in the laxity under the skin so your skin would feel tighter over the area injected. In the absence of any other symptoms, this is normal.