YOu got off the inhalers once already. Get the sinus infection under control first and then you can get off the inhalers the same way you did the first time. Eat paleo but this time, don't cheat so much. A lot of times with asthma, it can take time for the lung irritation and inflamation to slowly calm down. I have tried the herbals but all of them have been weak in comparison to big pharma's chemicals. Sorry if that is not paleo, but when it comes to strong asthma, that seems to be the case. Mild asthma can sometimes be controlled more naturally but moderate to severe asthma typically can't. My guess is that our environment has become so unnatural that our problems are sometimes very unnaturally bad.
Do not be ashamed to use your inhaler when you need it. Trying to stick it out can just allow the asthma to progress further and then it will take even stronger chemicals and more time to get it back under control again. I come from a family that is full of asthmatics. My experience is that asmtha is something you want to control early on and before it has time to progress. Often an early strategic tactical strike wins the battle early on and saves you having to bring in the heavier guns later. If the doc has suggested prednisone, then my guess is your asmtha has gotten rather bad. Prednisone is usually the fallback position when other stuff is not working. Prednisone can stamp down a nasty asthma attack like nothing else, but it has the side effect of damping down the immune system as well, which will slow recovery from the sinus infection. Once your asthma comes under control, try to slowly get off the prednisone so long as your other asmtha meds can pick up the slack.
Perhaps a better strategy of attack here is what can you do to get rid of a sinus infection as soon as possible, so that your lung irritation will also calm down. The only thing that has worked for me is healthy living and a bit of walking each day, as long as you are up to it (ie can breath enough to handle it). I'd also go to fitday.com and input food intake to make sure your intake is not low on any impt nutrients, which would also slow recovery. And get plenty of sleep and rest and try not to stress.