This app was mentioned in 3 comments, with an average of 1.00 upvote
Here are some that I know of. Note: All links take you to the game's official website, YouTube (for trailer), and Dekudeals, an amazing website that helps you find the lowest price point for a specific game (on game consoles), and figure out when would be the best time to buy.
--------------------Interior Design---------------------
House Flipper || Trailer || DEKU - House flipper is not a game about dressing up characters, but your game objective is to renovate and fix up a run down house to sell for profit. I really like the details they put into the game, such as the plumbing, and screws that you actually have to use to put things together.
Ark: Survival Evolved || Trailer || DEKU - I've been recommending this game quite a lot, because it holds a little bit of every genre you can think of. I'm adding this to the list because there is a building / design your own base feature where you have to go out, collect resources such as wood, stone, or metal, and craft building pieces yourself to build our own base. I mainly play this game on Steam/PC because it has various cosmetic mods for me to get more creative with different building pieces, but Ark is mainly a survival game, so there are other factors such as starvation, thirst, and temperature.
Terraria || Trailer || DEKU - This old classic is a game mainly about adventuring, but it has building being creative as an element to the game. I've seen so many creative builds, that it fascinates me a lot. I've yet to finish this game, but I look forward to picking it up again someday.
Airborne Kingdom || Trailer || DEKU - This is a city builder game, but you build your own kingdom in the sky and expand / branch out, and managing your kingdom that lives in the skies.
My Universe - Interior Designer || Trailer || DEKU - This game is almost like the house building feature from The Sims franchise. You basically design homes and find many different designs and styles. There's minigames to play to add more designs to your library. It also comes with character customization so there's a bit of a dress up feature that you're looking for.
-------------------------Dress up------------------------
My Universe - Fashion Boutique || Trailer || DEKU - It's a game about the dreams of becoming a fashionista. Design your own clothing to start your own line in branding and find a perfect fit for your patrons.
SELFY COLLECTION The dream fashion stylist || Trailer (note: this is a short review, since I couldn't find a trailer) || DEKU - This cute game localized from the JP e-shop is about aiming to become the top fashionista. It reminds me of an old dress up app I used to play known as LINE PLAY
Miitopia (DEMO AVAILABLE!) || Trailer || DEKU - I'm pretty sure this game isn't only about dressing up or avatar creation. I've never played it, but given the fact that you can dress up your avatar and go on adventures with friends, I think it's somewhat close to an avatar dress-up game.
>sadly they've all been shut down now.
Fantage has an unofficial rewritten version for single player only. You can check it out here:
https://www.reddit.com/r/Fantage/comments/hje617/fantage_single_player_now_released/
Otherwise, the only app I can think of is either Sims mobile or Line Play || Android || Apple