I've bought a Player's Handbook in the local gaming store. Now, I've tried to create my character online on D&D Beyond rather than on a traditional character sheet, but it wants me to buy a digital copy of the PHB to be able to give my characters subclasses such as the Totem Warrior for my barbarian. Is there a way to register my PHB on D&D Beyond to gain access to these subclasses without having to buy a second PHB in the digital version?

Nope, there is no connection between your physical purchase and the digital content. You have four options:

1. Purchase the PHB on DDB
2. Purchase just the Totem Warrior subclass on DDB (plus any other options such as race etc) that you need
3. Join a campaign that has content sharing enabled and someone owns the content you need
4. Using your physical PHB as a reference, use the homebrew tools to recreate the content you need for free, personal use.

D&D Beyond is a different company than Wizards, which still has to pay a licensing fee for the books.

See this thread for more information and the value you get

This question has been asked and answered so many times. It is on 2 different pinned FAQ threads, the support FAQ, has been asked 3 times this weekend, and hundreds of times further back.