What's that tool that doctors use to open your nose when you have a checkup after a rhinoplasty?

I believe you are referring to a nasal speculum.  At 5 months, it would be very difficult for a surgeon to ruin your results by inspecting your nose with this tool.  No need to worry.

The instrument you're referring to is called a "nasal speculum." It is highly unlikely that utilizing the nasal speculum (especially 5 months after surgery) led to some internal damage. In my opinion, you can rest assured that everything is fine. I personally use the nasal speculum carefully already 1 week after surgery without problems. Best wishes!

Great question.  What you are asking about is called a nasal speculum.  They come in varying sizes and shapes and are used to evaluate the internal aspects of the nose (as you have already experienced).  Using this will not change the appearance of your nose.  At 5 months post op it may still be a little tender in some parts, but do not worry.  It will not shift your septum or change the position of the cartilages.  Whenever we look in the nose after a rhinoplasty we make sure to do so very carefully and use the instrument just enough to be able to see inside clearly.  Otherwise it sounds like you are doing well and happy with the results thus far! Congratulations on your rhinoplasty and I hope you continue to do well. Good luck!

The instrument is called a nasal speculum and will not ruin your rhinoplasty results. It is noral for your surgeon to look inside. 

When you go to the doctor's office, they may use a nasal speculum to get a good look inside your nose. This device uses two blunt tips to gently spread open your nostril for a better view inside. With good technique, you should feel stretching but never pain.