Just got a rhinoplasty and now I’m reading horror stories online. How often do they really happen and why?

In general, these complications you speak of are very rare.  I would caution you against worrying too much and reading too many stories online as it will only cause anxiety.  It sounds like you did your research prior to your surgery and you likely chose a wonderful surgeon.  If you notice anything that seems concerning regarding your healing, contact your surgeon.  Otherwise, please try not to worry as you will likely be very happy with your results.

Yes, I would try not to worry. It's still too soon to tell what your final results will be. You need to have patience with your body as it begins to heal. The skin, bone and cartilage are all traumatized during surgery. Inflammation (swelling) is the normal response and will help your nose to heal and look beautiful in the end. If, one year from now, you are unhappy with your nose, then that is the time to think about a revision procedure. Right now, concentrate on other things you like to do and let your nose take its time to heal. I hope this helps.

Keep in mind, these complications are extremely rare and it sounds like you had your procedure performed by an experienced Doctor. You have to give yourself some more healing time.  Your nose and surrounding areas are going to be swollen for a while and you should be consulting the surgeon that performed the procedure but give yourself some time before going back in so some of it can subside. It can take up to a year for final results.
Sincerely,
Philip J. Miller, MD, FACS Double Board Certified Facial Plastic Surgeon

Rhinoplasty is probably the most
difficult cosmetic plastic procedure to master. While an experienced
surgeon will have a lower rate of minor and major complications after
surgery, and better looking outcomes overall, even the most experienced
surgeons have cases that look great on the operating room table, and
then evident imperfections afterwards. 
You can minimize, but not
eliminate, your chances of an untoward outcome by selecting a
meticulous, experienced, rhinoplasty expert.