I don’t have any space on my phone

You cannot increase storage of iPhone. However, you can optimize iPhone Storage by using iCloud Storage. Save space on your device

Settings > [your name] > iCloud Tap Photos > Choose Optimize [device] Storage Set up and use iCloud Photos - Apple Support

You can buy iCloud Storage. --> Buy more iCloud storage - Apple Support

You can manage your storage --> How to check the storage on your iPhone, iPad, and iPod touch

Manage your Storage --> Manage your photo and video storage - Apple Support

Your photos are always available for both iPhone and iCloud. You delete it on iPhone it is gone from iCloud and vice-versa. To save space on your iPhone use optimized iPhone storage. Remember, if you delete in one it is deleted everywhere.

Get started with iCloud Photos:

1. Tap Settings > [your name] > iCloud > Photos.

1. Turn on iCloud Photos.

1. Select Optimize iPhone Storage to save space on your device.

With Optimize Storage, smaller, space-saving photos and videos are kept on your device while all of your original, full-resolution versions are stored in iCloud. And as long as you have enough space in iCloud, you can store as many photos and videos as you want.

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