Will look like a rabbit if I undergo a bullhorn lip lift? (photos)

There are surgical and non-surgical approaches to lip augmentation. Non-surgical approaches include botox (slight lift, reducing gum show) and filler (volume restoration). Surgically, you can have two separate incisions under the nose (italian), one incision under the nose (bull horn), one incision at the red/white upper lip junction (gull wing) or two separate incision at the corners, or a combination, depending on your desired look and anatomy. My preferred surgical technique is called the Elelyft, which is a version of the bullhorn approach. 
The ideal candidate for the Elelyft, or upper lip lift, is someone with a philtral length of 13mm or longer, no upper dental show, and/or a thin upper lip. The nasal base to mouth width ratio needs to be taken into consideration to avoid leaving the lip corners down. 
In your situation, it's important to review before and after photos of the doctors you are considering for a lip lift to see if other patients have acquired the look that you fear. You do have upper tooth show already, which will increase with a lip lift.
Consult with an experienced lip surgeon for a complete range of options that are appropriate for your situation.
Gary Linkov, MD
Lip Specialist / RealSelf Lip Lift Medical Reviewer
Manhattan

I would have the silicon removed and not do the lip lift, then you can use fillers or use fillers alone to camoflage. In the mean time use lip plumpers and hydrators to make the lip more "swollen" and camoflage the silicone (see link to lip essentials kit at emeragecosmetics.com) Best, Dr. Emer.

That disfigurement is essentially irreversible. Given that you are already unhappy with prior lip treatment, does it make sense to double down with another potentially disfiguring procedure. Professionally, I think you have a lovely lip. Have you ever thought to step back and ask yourself if your concern about your lip makes sense or if the desire to change it is simply self destructive? A psychologist can sometime be helpful to grain personal insight about how you see yourself physically and emotionally. That might save you from a lot of unsatisfactory surgery in the future.

If you've had silicone in the lips, then a lip lift is probably not for you.  Silicone becomes lumpy with inflammation even years later and this can create an abnormal appearance.  The best treatment is to decrease the inflammation with steroid injections, and in some cases, to remove some of the silicone and scar tissue.  After that, a lip lift could be a benefit.