Hello and thanks for your question.
A watery eye is usually due to one of a few problems: 1. the eyelids not being positioned correctly (surgery, trauma, skin loosening as we age or a Bell's palsy can cause this); 2. There is some inflammation inside or on the eye (corneal scratches or infections and/or iritis) and the eye responds by being light-sensitive and also waters. This is usually not a chronic condition, but a solitary event; 3. Tear drainage obstruction or 4. Dry eye.
By far dry eye is the most common cause of tearing. It sounds backwards to attribute tearing to a dry eye, but when the eye is dry, the eye sends a signal to the brain that tells the eye to water, but the watering is usually not sufficient to keep the eye hydrated over the long haul. There are many reasons to have a dry eye. Some of the most common are: not making enough of your own tears, having eyelid inflammation called blepharitis, allergies, living in a dry/windy/dusty environment and some medicines (antihistamines commonly).
One of the first things to do to start treating dry eye is to start using artificial tears 4x/day for a few weeks. It must be consistent, daily use, however, or it won't work. Then, if there is mattering or crusting on the eyelashes in the morning and the eyes burn, sting or feel more irritated in the morning than the evening, then a daily regimen of hot compresses on the eyes x 10 minutes, followed by scrubbing the eyelashes with a dilute baby shampoo solution will help treat eyelid inflammation. If these things are done consistently, it is likely that you will have a noticeable improvement, but you must be consistent about them.
Knowing your history of a broken nose, however, there may be congestion and even inflammation or infection in the sinuses/nose from this distorted anatomy. This can cause a back-up of tear drainage which could cause this weeping. So it is possible that this is playing a significant role. However, I would suspect that if your doctor prescribed a nasal spray designed to open the nasal passages and this hasn't worked much then this is likely more due to dry eye than tear drainage obstruction. Also, the fact that you get styes means that you do have some of this eyelid inflammation (blepharitis), so I do think doing the above therapy for it would be useful to you. Something important to remember, however, is if you are supplementing your dryness with artificial tears, but aren't treating the inflammation causing the dryness, then you won't see an improvement in the symptoms. The lid scrubs and compresses have to be done concurrently with the artificial tears for 3-4 weeks before tapering down on the artificial tears.
Does this make sense and does this help address your concerns?
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