My phone is giving me a problem with managing photos and videos

You cannot increase the storage of an 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 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 the 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

Look closely storage of iPhone and iCloud.

You cannot increase storage of iPhone. However you can optimise 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

iCloud storage is primarily for keeping a copy of your iPhone data safely on cloud. If you delete data on iPhone, data on iCloud is gone.

iPhone Storage (Setting > General > iPhone Storage)

1. Total storage remains same through out life span of the iPhone
2. Storage can not be enhanced
3. You may take back up on Mac or PC using iTunes without iCloud

iCloud Storage (Settings > [Tap your name] > iCloud)

1. By default every user gets 5GB of free storage space
2. You can buy more storage based on your requirement 50, 200GB, 2TB with monthly subscription
3. Based on your storage capacity you can back up iPhone or iPad
4. The space can be shared between your family members for storage plan beyond 200GB