Alarplasty for High and Flared Nostrils?

Although I am not sure you can have a nose as narrow as Janet Jackson, you should certainly be able to accomplish your goals. An alarplasty alone just wont get you there. You would need a comprehensive Rhinoplasty and a good amount of patience to achieve that sort of look. The pro and cons of your nose towards your goals are:
Pros:

You have medium thickness skin, which will over time allow for definition and narrowing. If your skin was overly thick, then you often do not get as much as you want. With medium thickness, you get there but it just takes more time
You appear to have strong enough tip cartilages to work with
The overall width of the nose is not severe

Cons

You have medium thickness skin
You will require cartilage grafts to the bridge and tip to provide extra height and support
Your tip cartilages are 'cephalically oriented' which is mostly the reason that your nostrils arch so severely. Cephalic orientation means that the cartilage in the upper part of your tip points more towards your eye than it should. When cartilages point more towards the ear, they support and flatten the nostril. Adding alar rim grafts should help to flatten the nostril margin.
You still need an alar base reduction

Adding a profile view to your question would help to analyze your nose. However, no picture replaces a consultation/examination.
Good luck

Nostril reduction surgery (called Alarplasty / Alar Base Reduction) is a procedure that can narrow the width of the nostril base, decrease the amount of nostril flaring, or decrease the size of the nostrils.
To accomplish this, the surgeon makes an incision in the crease where the nostril wall meets the cheek. A wedge shaped piece of nostril wall is removed, and when the incision is sewn closed, the nostril narrowing is achieved.
It is possible to perform this procedure alone or as part of a rhinoplasty. It can be performed alone, but keep in mind that in order for the nose to appear natural, it must adhere to certain proportions and also be in balance with the other facial features

The nose type and appearance you are requesting may require a complex procedure at significant expense.
The heighten the bridge you will require a graft (ear or rib) or less preferably an implant.
The nasal tip will have to be built up to match the new bridge as well, This may require grafts from the septum or ear.
The ala (nostrils) will likely require an alar base reduction as well as a graft along the lining to bring them down and reduce the high rims. This may also need to be obtained from the ears.
No one is trying to discourage you but you must be prepared for the magnitude of the procedure as well as the associated risks.
Seek a consultation with a qualified surgeon.