Lelsie, you don't tell us much about your problem in your first post. We need to know a little more detail and the best way is to describe in steps what you tried to do on what (eg iPhone/laptop) and what happened.
Having said that though, if you are running short of storage space in iCloud deleting messages is not going to free up much space. Unless you have a huge number of messages and MMS images to delete.
Ashwin's suggestion above is a good one if you are just on the free, entry level 5GB iCloud storage, $0.99/month for 50GB is pretty reasonable.
Of course I don't know what settings you have but on my iPhone I have set "Keep Messages" to 30 days. This means they are deleted after 30 days. You can set to 30 days, 1 year or Forever. Personally if I haven't seen and actioned or saved data from messages in 30 days I probably don't need it.
Note; If you change the setting (Settings > Messages > Message History > Keep Messages) to one year or 30 days that will automatically delete all older messages. Later you can always set it back to Forever if that's what you want.