Is my nose damaged or fractured ? (Photo)

Yes, your nose is damaged. Perhaps, your nose is fractured. This maybe, just maybe, might need some sort of fixing. See your local doctor. They will need to feel and see your nose, and maybe get some form of X-ray or scan, to decide if you need to be seen by a specialist. 
Alternately, if the shape and function of your nose is not a massive deal to you, swallow a cup of concrete and harden up. Leave it alone to heal and be more careful around umbrellas in the future. 

Thank you for the question and photo, but the only way to truly know the extent of the damage to your nose is through an in-person consultation with an experienced, board-certified facial plastic surgeon. If there is a fracture or other damage, early intervention typically produces the best result. It doesn't necessarily prevent the need for rhinoplasty in the future, but it does lower the likelihood you will need additional surgery later on. Get it checked out now for the most effective treatment options and your own peace of mind.

With the symptoms you have and the swelling on your photo, the best thing to do is to be seen by a doctor right away - head to your local urgent care or ER.  It is possible you may have a nasal bone fracture, but you may have other injuries as well.  Headaches after a face or head injury could be a sign of concussion. If you are diagnosed with a nasal fracture by an X-ray or CT scan, you should see a facial plastic surgeon, ENT or plastic surgeon within a week.  If it is a displaced nasal fracture a closed reduction can be performed within the first 10-14 days after the injury that can get the bones aligned back into their original position.  If you wait longer than 14 days the bones will have started to heal and be unable to be reduced easily.  If the fracture is not addressed within the first 2 weeks, it can be fixed by a traditional rhinoplasty once the bones are fully healed a few months later. 

If the nose is not deviated, and your breathing is unchanges, probably it is not a major injury. It is close to impossible to know if there is a fracture unless you get a CT or MRI. Give it some time, unless you have one of the symptoms above, then I would go see a specialist right away.

Sorry for your trauma. There is a probability that your nasal bridge (bones and cartilages on top of your nose) may have been broken and/or have a greenstick fracture (not displaced). The best way to manage this would be to have a full examination in combination with a direct nasal x-ray or a CT-scan if required. If displaced you will need immediate reduction, if not cold treatment and elevation of your head would be enough. Nevertheless, deformities may occur with time which may require a rhinoplasty to correct for aesthetic purposes.
Hope this helps,
Ali Rıza Öreroğlu, MD FEBOPRASEuropean and Turkish Board Certified Aesthetic, Plastic and Reconstructive SurgeonIstanbul, Turkey