Can I transfer things from my phone to iCloud? I’m asking because my phone’s storage is full.

See the following from About storage on your device and in iCloud - Apple Support

You can make storage space available on your iPhone, iPad, or iPod touch when you use iCloud Photos and turn on Optimize Storage. Or you can remove content from your apps—like photos, music, and Podcasts—or delete the apps that you're not using.

No, iCloud storage will not increase the storage capacity of your iPhone. Read these three Support Articles for an explanation:

1. About storage on your device and in iCloud - Apple Support
2. How to check the storage on your iPhone, iPad, and iPod touch - Apple Support
3. About storage on your device and in iCloud - Apple Support