How Can I Fix my Turned Up Nose?

From the description, it sounds like the best option to correct these issues is rhinoplasty.  This can be accomplished by counter-rotating the tip so that the nostrils do not show as much on frontal view.  If your bridge (dorsum) is overly sloped, augmenting this area also may be necessary.  A detailed exam would be necessary to formulate a plain specifically for your anatomy, but it would generally involve cartilage grafting and suture techniques.  Fillers are not a good long term solution to this problem.  See a rhinoplasty specialist who can evaluate your anatomy and go over photo simulations to make sure you have the same shared goal in mind.

The situation is a little more challenging than the standard rhinoplasty with a dorsal hump. If you have never had rhinoplasty then this is probably due to a congenital short nose. Cartilage grafts can be used to lengthen the nose or just the tip if that is all that is needed. The cartridge can be harvested from the septum which is the dividing wall between the nostrils. This may be a situation where a closed rhinoplasty is better since the placement of the grafts places tension on the skin of the nasal tip. This would place tension on the suture line in the open technique. A careful assessment by an experienced rhinoplasty surgeon is essential in order to get the best advice. Photographs would be helpful.

There are a number of different techniques to fix an upturned nose.  It would be very difficult to describe exactly how the different procedures are done, but I use an open rhinoplasty approach to allow the tip of the nose to be derotated so that the nose is a bit longer and the nostrils are less visible.