There is no Cachly membership, only a geocaching.com membership. There's no Cachly user account in the app, only a geocaching.com account.
If you purchased a premium membership on geocaching.com, you will have full access on the site and be able to view unlimited caches through Cachly. Did you buy a membership on geocaching.com and provide your credit card info or Paypal info? If not, you still have a basic free account. If you paid, then log out and log back into your account on geocaching.com and see if it shows you as Premium at https://www.geocaching.com/my/ . On the top right where it shows your Finds and Hides, above that it will show Premium Member.
If geocaching.com shows you as a premium member, log out of your account in Cachly and then log back in and you will have full access to caches from within Cachly.