Hi Anne. 
It would be interesting to know what was performed in your primary rhinoplasty, and what the before and after photos look like in regards to the primary procedure. Information regarding what's been taken out, added, or adjusted can help to explain the current appearance of the nose. Additional oblique and worms-eye (from below) photos would also be helpful. 
I can understand your perspective. The tip of the nose is bulbous in nature, with a "parenthesis" - () - deformity. This can sometimes be due to upward mal-positioning of the lower cartilages of the nose. Your Alars (nostril wall) appear to be slightly retracted in the photos, together with some droopiness of the tip. Whether this is static (there all the time) or dynamic (only when smiling), is difficult to determine.
Revision rhinoplasty in general is more difficult than a primary procedure. It carries more risks and potential for complications. The thickness of the skin does play a role in outcome. Swelling is usually more prolonged after surgery in thick skin noses and definition is harder to achieve. The important factor to any rhinoplasty, primary or secondary, however, remains the creation of a solid framework and long term support for the nose.  
I hope this helps.
Kind regards,
Dr Ray Goh