Inquisitors do not spread their religion to other cities -- they just stamp out other religions. If your religion was never present in a city (i.e., it got converted away from you before you could convert it), an inquisitor is only half the solution. Pair a missionary with the inquisitor -- zap the city with the inquisitor to cleanse it, and then use the missionary to spread your religion.
BUT, as myclan notes, you must buy the inquisitor and missionary in a city that that is majority your religion. If you buy them from a city that is majority someone else's religion, you will be spreading and/or reinforcing their religion, not yours.
If your religion is not majority in any of your cities, you may be out of luck. You need an apostle of your religion, and the only ways to get those are to build Stonehenge (if you've founded a religion, gives 1 apostle) or Mahabodhi Temple (gives 2 apostles), but neither may be around at that point in the game. And if you do get an apostle, don't bother reconverting any of your cities until you have a stockpile of faith and have a temple in the city (so you can quickly buy more apostles of your religion, as well as inquisitors of your religion).