Hi Barbara,
What is the version of Adobe AIR you are trying to install? There will not be any icon available for Adobe AIR if you are expecting the same. Could you once download the latest version of Adobe AIR from Adobe - Adobe AIR and try to reproduce with the same. If it says that the installation was successful try running .air app and if you observe any issues take a screenshot of the same and post it here so that we can understand the issue better.
Thanks!