Hey! I finally graduated college at 24 so I sort of get where you're coming from. As long as you're not shopping at Baby Gap I don't really think you need to worry about dressing "too young". No one is going to point at you and say "Hey! Look at that 22 year old wearing an outfit meant for a 20 year old!" They'll probably just think you're outfit is cute!
As for places to shop, I'll admit I tend to mostly shop at "fast fashion" retailers. Forever 21 can have some good stuff but it can definitely be hit or miss (especially for the style you've linked to). H&M is great for basics/muted clothes but I personally don't have an H&M with a plus section near me. I'm a size 16 and fit into some of their straight sizes so that isn't always an issue for me, so it just depends on your fit and if you prefer trying things on in a store!
When the world isn't in chaos I also like to thrift for more "professional" clothes. They're usually cheaper than the trendy stuff and more easily accessible in larger sizes at thrift stores IMO. Most (if not all) of the thrift stores near me in the north east sort by size but I've seen in other threads that that usually isn't the case so you may have to hunt a little. Places like Plato's Closet tend to cater to a more high school demographic but don't count them out for things like cardigans, sweaters, dresses, etc. I got a Calvin Klein cocktail dress for like $12.
I hope this helps at least a little!