Runny nose after rhinoplasty - Could the surgery have caused this issue?

Runny nose a year post-op is not considered normal. The situation may / may not be related to your operation, and needs to be investigated. A physical&endoscopic examination should be conducted to see if there is any anatomic blockage (deviation, turbinate hypertrophy, synechia, polyps etc), and you should also need to be evaluated for any chronic sinusitis. You'd better refer to your surgeon.

Drainage from the nose after a rhinoplasty is most likely due to residual mucosal inflammation.  As it resolves drainage may occur. However, for this to persists for 1 year after is unusual.  There may be chronic sinusitis from the maxillary sinuses, and some imaging may help elucidate this.  There may be a synechia or some form of mucosal scarring that entraps drainage.  A rare cause is a CSF leak and this can be elucidated by evaluating the drainage itself. You need an internal exam of your nasal passages and some imaging to understand the issue better.  

It would be impossible to really know what is going on without a full evaluation and looking inside your nose. There are numerous causes of a runny nose, so there could be other sprays that work more than the ones you already tried. Rhinoplasty only fixes the structural issues with breathing and doesn't address any allergies or irritants in the air. I sometimes see more drying after surgery since more air is getting in, and I recommend AYR gel with aloe in that case. With some bloody mucous coming out that's definitely part of the issue. 
Even if you never had allergies before, every environment and year is different. If you moved to a new city or if that year was particularly rainy you could have more mold or weeds. There is also a type of runny nose called nonallergic rhinitis that has nothing to do with pollen or allergies.
As you can see there are many variables, so any advice is clearly speculative without a full history and physical exam. 
Best of luck to you,
Sarah Saxon, MD