You can certainly have rhinoplasty to address only the tip, while leaving the bridge alone. No osteotomies are needed so there's minimal to no bruising. It's still a surgery, but much less invasive than a full rhinoplasty. Be sure to see a rhinoplasty expert for consultation.
You are a good candidate for alarplasty. The minimum time you should wait to get alarplasty is 3 months after your rhinoplasty but the preferred wait time is one year. Your nose will continue to change for a whole year. There is likely some swelling in the tip and will get better over time....
Yes, it is possible to reduce nostril flare without excising nasal floor. If the nostrils still seem flared to you, a wedge can be removed only from the lateral nasal walls to correct this.
