Can a septorhinoplasty with columella correction help me get the concave upper lip without lifting my tip too much?

A septoplasty is performed in the back of the nose to improve airflow dynamics and is performed for functional purposes and will not change the shape of the nose. A rhinoplasty procedure can accomplish making all the required changes to the nose such as reducing a hanging columella, shaving down a dorsal hump, narrowing the bulbous tip, and narrowing the bridge line.  A septoplasty and a rhinoplasty will not make the upper lip any different. For more information and many examples, please see the link in the video below

Although pictures would be helpful, it sounds like you are asking for your columellar position to be adjusted without rotating the nasal tip. This can be performed via a rhinoplasty. 

A difficult question to answer without having the opportunity to evaluate your nasal labial angle, the relationship between the columella and the upper lip.  A lateral photographs would certainly have been helpful in this endeavor. If there is a very  obtuse, open,  angle between the columella and the lip  improving that angle can improve the height and  depth of the lip and the relationship with the projection and rotation of the tip.  The tip does not have to be turned up in order to address the relationship of the nose with the upper lip.  Addressing the relationship between the nose and upper lip can occasionally disrupt the muscles that lift the central portion of the lip when smiling that can lead to a temporary change in the smile which will resolve over time but may take as long as 6 months to completely resolve.