Would I be good at artistic gymnastics?

As a new starter at 16 your build isn't really going to be that important to your progress in artistic gymnastics (unless you were obese which doesn't apply.) There are a lot of factors that contribute to success, natural talent, balance, coordination, strength, flexibility, ability to take direction, work rate, dedication and yes, build. But build and height are about the least important out of all that. They matter at high level because everything matters at high level. For you though it just isn't going to be important.

Artistic takes more strength than rhythmic and a lot more power. (This does inhibit flexibility for dance which is why career ballet dancers won't do gymnastics but again this becomes more of an issue the more training and higher level you are in either activity and is not a problem for a beginner or someone doing gym and dance for a fun hobby.) Those are both things that you can develop to a good extent through conditioning. Similarly rhythmic requires good static strength and great flexibility and coordination which you can train and improve. One or the other might come more naturally to you but you could improve at either.

So you could certainly do artistic gymnastics and improve at it and learn new skills. Starting at your age you won't be competitive in either artistic or rhythmic so you really just should pick whichever you think you would most enjoy. If you are going to keep up dancing you might want to artistic for more of a contrast. If this is instead of dance you might want to do rhythmic because it is dance based. If you want to do a sport where you work in a team you might prefer cheer, team gym or acro (though there are group routines in rhythmic too.) A lot of sports classes will let you do your first session without commitment as a taster (sometimes free or sometimes a pro-rata fee.) It would probably be a good idea for you to take advantage of that to get a better feel for what the classes are like and help you decide what you would most enjoy.

I know doing Dance, Cheer, and Gymnastics can all be pretty expensive (but usually if people CAN afford this, they have sponsors to help them out a bit, which is what most Olympians do), so I obviously wouldn't recommend doing all of them. But would I would do is take a "trial" (when I tried different sports, they usually said the first one was free, and if I had enjoyed it, you just keep going from there.) of all the sports that appeal to you best, and THEN figure out what not only your BEST at, but also, what YOU enjoy! Sports are meant to be fun, so choose what YOU love best! Also, having ALL of your splits will be VERY HELPFUL no matter what you choose!

Another sport you could mate try is figure skating. I know how much I loved to ice skate, and if your like me and don't have a rink nearby, you could try using rollerblades the same way! I know a friend who actually does it!

PS! Age and height doesn't really matter unless there is some sort of limit to some sort of competition.