How can I add more storage without deleting things

You cannot expand the storage of your iPhone.

1.

You can try to free up iPhone device storage see this Apple articles below:

If you need more space for an update on your iPhone, iPad, or iPod touch

If you need more space for an update on your iPhone, iPad, or iPod touch - Apple Support

How to check the storage on your iPhone, iPad and iPod touch

How to check the storage on your iPhone, iPad and iPod touch – Apple Support (UK)

Clear Other storage on your iPhone or iPad

Clear Other storage on your iPhone or iPad - Apple Support

2. 

If you wish, you can upgrade the 5 GB free iCloud.

See -> What's the difference between device storage and iCloud storage?

What's the difference between device storage and iCloud storage? - Apple Support

See also the following Apple articles:

Upgrade to iCloud+ -> Upgrade to iCloud+ - Apple Support

iCloud+ plans and pricing -> iCloud+ plans and pricing - Apple Support

How to use iCloud on iPhone -> How to use iCloud on iPhone – Apple Support (UK)

Manage your iCloud storage -> Manage your iCloud storage - Apple Support