Can my broken nose and frequent headaches be related?

Yes, it is possible they are related, a broken nose and a broken septum can create a shelf and bone spur formation in the back of the nose  which can cause headaches.  Chronic sinusitis can also cause headaches.  A CAT scan of the sinuses and nose is required to make a determination about how best to proceed.   A cosmetic rhinoplasty is required to straighten the crooked nose, a septoplasty is required to straighten a deviated septum, and endoscopic sinus surgery is required to remove polyps that are creating chronic sinus infections and headaches.  For more information and many before and after examples, please see the video below

Hello m.s.r16,
Trauma to the nose can create obstruction or blockage in the nose making it difficult to breathe. It can also lead to pain or headaches if structures inside your nose are now too close together and are touching, instead of allowing passage of air between them. Also, you may have sinus blockage that can contribute to facial pressure or cause pain and headaches. A CT scan and nasal endoscopy can help delineate what's going in your nose and sinuses. You can schedule a consultation with a facial plastic surgeon (someone who has a background in ENT-Head and Neck Surgery with further subspeciality training in facial plastic surgery) - some of us evaluate the sinuses and perform sinus surgery if needed in conjunction with reconstructive and/or cosmetic rhinoplasty. Alternatively, you can see a facial plastic or plastic surgeon and an ENT separately. 
I hope this helps, and good luck!