My phone icon does not appear when I connect my phone to my computer. The problem developed after updating to current version 9.3.1. This prevents me from syncing new music, etc. The icon for my I-pod does appear and I am able to sync music from the library on my computer to my I-pod.
What computer OS are you using. iOS 9.3.1 requires the latest version of iTunes, which is 12.3.3. That version of iTunes has specific computer OS requirements, especially for OS X. If you are using OS X, what version are you using?