Will my upturned nose will drop into a normal range? 1 month ago post-op. Very disappointed. (photos)

Being a solid truth you are in a too early stage and lots of changes (likely improvements) are bound, sure.
But let me suggest researching about the following:
-short nose rhinoplasty
-septal lengthening 
-lowering nasal tip
-the so called "tension nose"
As per your preop images and if you consulted me directly or you posted here a preop question, I'd have you know the following:
-you have a short nose and a short septum syndrome, associated with a tension nose
-itselt, your nasolabial angle, angle between columella and horizontal plane, is too wide, it is about 45º and as maximum 10-15-20º (depends each face), itself and now, before surgery, already needs an ambitious lowering by means of septal lengthening, grafting of tip, eventual grafting or alar rims, etc
-but even if you wanted to retain the same upturned tip and nasolabial angle, in case you loved it... I'd also have you know that this is impossible without specific maneuvers, because shaving your dorsum involves shaving its caudal end (of the dorsum) and this includes the tips of the lateral upper cartilages, therefore shortening further on the nose and upturning the tip another additional 10-20º, which would be a piggy nose
-so I'd advise and indicate a conservative septal and nasal lengthening in case you wanted to keep the same nasolabial angle and upturned tip... or an aggressive and complex one (likely covering alar grafting as well) if you wanted to lower a bit your nasolabial angle and derotate your tip.
Seems your surgeon did a basic routinary and standard rhinoplasty, and seems very well done, but he did not apply any maneuver to prevent further shortening/rotation, neither to correct it if this was your wish.
Yes, improvements will occurr, and your result will be good indeed, but if you want to treat something else than your hump... then you have to perform something else than shaving the hump; in the future seek the opinion of a surgeon expert in complex cases, revisions and short noses.
Yours is the perfect example of a good standard rhinoplasty well done but not considering hidden problems or potential unwanted effects. It is a matter of experience, we all have learned lessons in life.
PS: you are a perfect case for a sliding genioplasty, awesome for you.

It is far too early to assess your results, as your nose will continue to shift and change over the next several weeks to months.  You may consider a sliding genioplasty or chin augmentation to assist with facial balance, as that will often change the profile in a positive manner.

Yes, it is still too early.  A few things are going on: there is still swelling of the upper lip which displaces the tip upward, and stiffness of the skin envelope which holds the tip unnaturally high.  If after 6 months you still cannot accept your profile then I would begin examining the options with your surgeon.