I can’t install the iOS 15.5 on my phone. It says I’m not connect to the internet even though I am.

Try first to optimize the range of the mobile network, see this Apple article:

If you see No Service or Searching on your iPhone or iPad

If you see No Service or Searching on your iPhone or iPad - Apple Support

👉 If you still don't have a 'service' after that, see -> iPhone 7 Repair Program for "No Service" Issues

iPhone 7 Repair Program for "No Service" Issues - Apple Support

Then try to update:  

See the following Apple articles:

Update your iPhone, iPad, or iPod touch

Update your iPhone, iPad, or iPod touch - Apple Support (IN)

If your iPhone, iPad or iPod touch won’t update

If your iPhone, iPad, or iPod touch won't update - Apple Support

You can do the update via PC, see this Apple article: Update software on iPhone, iPad or iPod touch in iTunes on PC

Update software on iPhone, iPad or iPod touch in iTunes on PC – Apple Support (UK)

If you have a Mac see this Apple article: Update your iPhone, iPad, or iPod touch with the Finder

Update your iPhone, iPad, or iPod touch with the Finder - Apple Support

You need about 7 GB device storage and good Wi-Fi.

If they are On, turn Off Hotspot & VPN.