If you have cough variant asthma it may affect your voice a lot more than your 'regular wheezy' asthma. I don't know that I've ever had troubles with steroid shot (I'm assuming kenalog?) and losing my voice, though I've only had one. Most doctors do not prescribe steroid shots anymore. If you are taking Advair or something like that it can give you a hoarse voice as well, but it should not be for more than a couple of days. My suspicion is more involved around Vocal Cord Dysfunction. Sometimes our vocal cords try to protect our lower airways and spasm on their own. This can cause bouts of coughing and can mimic asthma, even seem like hard-to-control asthma. If this is happening, you may end up coughing more, and it can obviously have a large strain on your cords. What is hard to determine is if you have asthma and VCD and if they're coexisting. I would suggest a methacholine challenge with a laryngoscopy for a diagnosis.

Here's some more info:

[url]http://nationaljewish.org/medfacts/vocal.html[/url]