Have you measured your Peaf Flow? I would suggest that you should take your blue/ reliever inhaler more often than usual until your coughing settles down. If you have been given a course of steroids you should complete it, and make sure that you are taking your steroid/preventer inhaler. If you do not have a course of steroids, you could/should double up your dose of steroid inhaler. If you smoke, I would suggest that you stop (completely or for a while anyway), and many apologies if you do not smoke.
Keep up the increased inhaler use until your peak flow improves, and if it is only a quarter of your usual number, then I would suggest that you should be back in hospital. The coughing is troublesome, but indicates that your airways are swollen and inflammed; steam will help, but the most important thing is to keep your airway/tubes open by increasing your inhalers as I have suggested.
i hope that you are better soon.