What can I do to improve my breathing after breaking my nose?

Medication v surgery. In the short term decongestants can help. For 3 days and 3 days only you can use an over the counter decongestant nasal spray such as afrin or neosynephrine. If you use it for more than 3 days your nose will become addicted so don't. Medications like sudafed can help. Prescription steroid sprays can help as well. Surgery may also be necessary. See an ENT doctor within a week of the injury.
Surgery. If obvious external deformity, surgery is probably best option. If newly broken and still swollen and no obvious external deformity, you could chance it and wait for swelling to come down, breathing may improve. If not, then you'll need surgery, and if you wait too long, bones may need to be re-fractured. Best to see an ENT sooner rather than later to get an exam and informed opinion.