Hi msknopf,
When you get the message about a software update, does the message specify if it's for your iPhone? Generally, when you connect your phone, iTunes will search for an iOS update for your phone and alert you if one is available.
Which model phone do you have, and what is its current iOS? Settings > General > About > Version (or Software Version)
If the message is referring to your Mac's OS, your MBP is an early 2015, which can be upgraded to the current OS (Catalina) through the App Store after making sure you've backed up your computer and have the power adapter connected.
The reason you're not getting OS updates is because you're probably at the top of your OS: 10.11.6.
You may have downloaded OS installers like Sierra, High Sierra, Mojave that may be sitting in your Applications folder.
If not, or you want to go straight to Catalina from your current OS, you can find Catalina in the App Store by searching for it if it doesn't show up in the Discover banner.