I purchased more storage space but when trying to download an app I’m still not able to, does anyone know why?

I would like you to realize and know one important thing and that is that there is NOTHING that you can do to increase the physical storage capacity of your iPhone. Your iPhone's storage capacity will forever remain the same as the day you bought it. 

You have purchased ➔ iCloud Storage from Apple where you may create and save your iPhone backups and synch (Not Store) your Messages, Photos, Contacts, Calendars, Notes and Reminders. Note that iCloud Storage is NOT an extension of storage capacity of your iPhone. Just wanted you to know some facts.

Having said that, you can choose to Optimize Storage on your iPhone for all the Photos. What this action will do is store your original quality photos on iCloud and a small size photo on your iPhone. This takes up less space on your iPhone while maintaining the actual size on iCloud. This will free up space on your iPhone while making good use of iCloud. If you would like to try this then open Settings ➔ Photos ➔ Optimize iPhone Storage : Ensure that this option is chosen and has a checkmark on it.

Axel F.

You need to purchase the extra iCloud storage but then take steps to move your data to iCloud. It will not do it by itself.

iCloud storage is independent of iPhone storage. If you need more space on your phone, you will need to delete something.

You purchased more iCloud space, not space on your iPhone. You cannot add storage space to your phone. Go to Settings > iPhone Storage and see if you have any Recommendations to gain some space.