Whooping Cough is also known as Pertussis. It is the P in the DPT immunizations that are given to children and pre-teens. They now know that the childhood immunizations we were given for Pertussis do not last into adulthood. At this time, there is not a standard recommendation from the CDC for adults to add this to their routine preventative schedules. It isn't even covered by all insurances. I know it isn't covered by mine. There has been a resergance of incidents of Pertussis in recent years. It is fairly contageous.
Pertussis is also nicknamed the 100 day cough. It is a long miserable 3 months. You can become worn down and more susceptible to picking up other things, but typically it is more dangerous for the very old, very young or those with other severe health problems.
I agree that the nosebleed sounds like it is probably from coughing so much. The other symptoms sound like they could be from the antibiotic. You should talk to your doctor. There may be another antibiotic you could use that doesn't have such bad side effects. Once you complete your initial round of antibiotics, you should be through and not contagious, but you will still have the cough left for a long time.
I had Pertussis a couple years ago. I had had it for about a month before it was diagnosed. I have sinus and asthma problems with a cough as a symptom. They just treated me for those before realizing what I had. Turns out the two rounds of antibiotics I was on for the sinus infection also treated the whooping cough when I first had it and didn't even know. The Pertussis flared my asthma up too so I was on additional asthma medication and steroids while also dealing with the Pertussis. My first Pertussis test came back inconclusive. They didn't know if it was because I had Pertussis or because of the immunizations I received when I was young. I had to go to the hospital for a special test to get a specific diagnosis.
With regards to the cough, it will last for a bit over 3 months. The first couple months are the worst, then it will gradually start getting better. I would cough so hard that I got lightheaded, vomited at times, pulled stomach muscles, hurt a rib and had some incontinence. It was extremely hard to catch a breath in between the coughs. I was often bent over almost double while coughing. Things were worse for me because it was winter and I had cold air triggering my asthma cough too. There were no cough medicines that helped at all. At one point, I did get some medication to help me sleep a bit, but I was scared to use it too much. I did keep sucking on mints, candy, cough drops, etc... to keep my mouth hydrated. I also made sure to drink tons of water to help. Aside from sinus and allergy problems, I never picked up bugs or got sick in that way. Hadn't most of my life. While I had Pertussis, I ended up with the flu and a viral infection that took my voice for a month. My body was just worn out. At one point, my doctor offered to hospitalize me if I wanted.
You will get through this, but it is miserable in the meantime. There isn't really anything else you can do other than endure. I've had not lasting effects post-Pertussis though.
You should be getting a call from your local health department. The CDC tracks cases of Pertussis and the health department will want to get some information from you. Also, if you have anyone around you who hasn't had the immunization, they may want to consider getting immunized. You may also want to get an immunization when you feel better too. This is not one of those things like chicken pox that builds immunity. You could easily get it again.
Good luck getting through this.