I think that at a minimum you should call your physicians office and speak with them, or if afterhours, the doctor on call and ask them for their recommendation. You might have simply injured tissue through coughing in the same manner you can get a small bloody nose through sneezing.
If you feel it is serious enough and you are having other symptoms, not getting additional relief from the inhaler (which is appears you did) you would probably want to call 911 as respiratory issues are serious and a stroll down to the ER could cause you to wait hours, whereas you are generally attended to immediately with an ambulance visit.
If you do not have an oncall doctor, are still concerned but do not want to go to the ER, try going to an Urgent Care center and informing them of your issue - triage might get you seen right away.
Nonetheless, please do not delay your visit because you fear "getting cut up." We all fear this... it is something that I would never want to have happen to me, but believe me if it is warranted, that means they are attempting to do emergency measures to mitigate a most likely life-threatening situation. My (albiet limited) understanding is that emergency room surgery is performed under only the most serious of cases - gunshots, heart attacks, etc. Most likely IF you do have an issue that warrants concern, you will receive an X-Ray to look for abnormalities/fluid buildup in your lungs.
I wish you the best.