I bought a monstrous race (Changling) because I wanted to make a Changling PC on the website, but there doesn't seem to be an option to create your own Changling, or any monstrous race character, on D&D Beyond, which sucks because I paid for this race and now my only option in to make a paper character sheet, but that defeats the whole point of buying it. It's be a great option to add to allow people to create online character sheets for non-traditional races. Thank you.

You can definitely make a changeling on DDB. Let me ask a few questions:

1. Did you buy the changeling race or accidently buy the changeling monster? (Actually, I see you commented in the monster's stat block, so that leads me to believe you bought the monster and not the race.)
2. Do you have eberron content enabled in the character preferences?

Quote from abbypsmiley >>

I bought a monstrous race (Changling) because I wanted to make a Changling PC on the website, but there doesn't seem to be an option to create your own Changling, or any monstrous race character, on D&D Beyond, which sucks because I paid for this race and now my only option in to make a paper character sheet, but that defeats the whole point of buying it. Thanks for reading

 
Aside from the fact you can buy a Changeling Race anyway, you can use the homebrew tools to make any race you want, you don't need to go back to using paper and pencil.

Buying Monsters doesn't suddenly have you make them as Player Characters, there's a difference between Monsters and Races. The Monster Manual doesn't give you them as new Player Race options, either, so I'm baffled as to why you think the same applies to the site.

If you want a Player Character race, buy the race. If you want a Monster the DM controls, buy the Monster. If you want a Player Race based on a Monster that is not available to purchase then make it with the homebrew tools.

But, the Changeling is available as a Player Race in the marketplace.