Can I add AppleCare to my phone that I've had for 13 months

No, you can not add AppleCare now.

No. It must be purchased within 60 days of the iPhone purchase.

The screen replacement without AppleCare+ is $149: iPhone Screen Repair & Replacement - Official Apple Support.

You cannot add the extended warranty to any Apple product once the original one year warranty has passed. All Apple extended warranties must be purchased and registered for the device within the original one year warranty period, and with an iPhone, within 60 days of original retail purchase.

You also cannot add an extended warranty to an iPhone that already has pre-existing damage.

Michael Black wrote:

You cannot add the extended warranty to any Apple product once the original one year warranty has passed. All Apple extended warranties must be purchased and registered for the device within the original one year warranty period, and with an iPhone, within 60 days of original retail purchase.

AppleCare+ for iPhones must be purchased within 60 days of iPhone purchase.