Flatten the underside/bottom of the nose between nostrils?

It sounds like you're referring to lifting up the columella. This is something that can be done during rhinoplasty. You can learn more about this type of surgery at my web reference link below.

 Hello and thank you for your question! This area can definitely be improved. Seek out an experienced rhinoplasty surgeon for best results.

Hello and thank you for your question.  The
best advice you can receive is from an in-person consultation.  Yes, it is possible to lift the columella with rhinoplasty.   Make sure you specifically look
at before and after pictures of real patients who have had this surgery
performed by your surgeon and evaluate their results.   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

A full set of facial and nose photographs required to make a determination about how to proceed surgically.  If you are referring to the hanging columella, then yes, a columella-plasty can be performed which can addresses this issue.   When patients have a hanging columella, the nose looks" bottom heavy". This issue can be addressed with a closed rhinoplasty by making all incisions on the inside of the nose.  No external incisions are required. Digital computer imaging  in the office setting would also be helpful to understand what can be accomplished with your nose upon your facial features.  For many columella-plasty examples and more information, please see the link and the video below

The structure you're probably talking about, is called the columella, which is routinely lifted as part of the rhinoplasty procedure when necessary.