Will an alarplasty give me a smaller nose as its very bulbous and my nose gets wide when I smile?

Based on the provided photos, your nose is wide, bulbous, and has poor definition. The nose in the "goal" photo you sent is narrow and has excellent definition. The only way to achieve those types of changes is through a rhinoplasty procedure to refine the nose throughout, not just at the alar base.
Be sure to see an expert.
All the best,

Hi,Thank you for including your photos. To start, you will never have the nose of the model you have included, not because there isn't a skilled enough surgeon but because of the anatomy of your nose (length of bones and cartilage, strength of cartilage, quality and thickness of the skin). Now you can have nice changes made to your nose with a rhinoplasty, but an alarplasty alone will not be enough. I recommend visiting with a rhinoplasty expert to discuss your aesthetic goals and review the entire process from start to finish.Best,Mehdi Sina, MD

Hello and thank you for your question. Based on your
photograph, you may benefit from a tip refining rhinoplasty. Your surgeon can
accomplish this by trimming, suturing, and reshaping the cartilage in your
lower nose. You may also benefit from an alar base reduction.  Make
sure you specifically look at before and after pictures of real patients
who have had this surgery performed by your surgeon and not just a computer
animation system. The most important aspect is to find a
surgeon you are comfortable with. I recommend that you seek consultation with a
qualified board-certified plastic surgeon who can evaluate you in person.
Best wishes and good luck.
Richard G. Reish, M.D. FACS
Harvard-trained plastic surgeon

The goal of an alar-plasty is only to narrow wide nostrils. That's it. If you want to narrow the entire nose, that is considered a rhinoplasty to narrow the bridge line, and the nasal tip cartilages

Based upon your photos, it appears you have a have a bulbous nose tip with wider bridge and nostrils than you would like. The bulbous tip would need to be reshaped; grafts may need to be used for tip support. You could benefit from nostril narrowing as well.  An alarplasty procedure will address nostril width only.  Ethnic rhinoplasty is by far the most challenging cosmetic operations in cosmetic surgery. This because the anatomy and skin thickness requires special techniques to achieve desired results. Do your research online and select a surgeon who can deliver results that you seek.  They should have numerous before and after photos with results you like. Choosing the right surgeon who has experience is imperative; you want to avoid any revision in the future. 
Best,
Dr.S.