I bought a digital copy of the players handbook this morning after having just borrowed a friend's and using the app to hold my character sheet. I bought the book today because I want to add a certain feat to my character. Now I have access to the whole phb on the Web browser but not the app. And in either setting I still can't use options from the players handbook in my character builder. I've read about content filters and such but The phb being core content I can't see any such filter. Also. My app user name doesn't include the random numbers and letters at the end so I'm wondering if somehow I've got 2 accounts on the same email. 

Probably the 2 accounts thing. 

D&D Beyond doesn't have it's own login system. It uses other account services: Wizards of the Coast, Apple, Discord, Google and Twitch. 

If you use one for the site and another for the app without linking the accounts together (which can be done here: https://www.dndbeyond.com/account ) then it will treat them as two separate accounts, even if they use the same e-mail address. You can see if it will let you link them but since you've created 2 it may no longer let you. Try and see. If not you will need to contact support which you can do here: https://dndbeyond.zendesk.com/hc/en-us/articles/360055233654-Contact-Information - it may take some time to get a response, especially right now, so please try to be patient.

Once sorted, I highly recommend linking all such services into one D&D Beyond account to prevent such a thing happening again in future.