You are fully grown at age 23. You will not get taller. Why do you worry, you are just over 5ft 6 inches ? (if my conversion is correct) That is a good height for a female.
No you are usually full height by 23. I'm 5'7 and I find it's a good height, slightly on the tall side of average. If you're thinking of things like modelling plenty of models these days are shorter than they used to be, you really don't have to be a 6 footer anymore, if it's another job then I don't know, but 5'6/ 5'7 is fine so please don't worry.
Your height is about average in the UK, above average in some countries and below average in yet other countries. You will notice that everyone mentioning their height in their responses do so in strange symbols, but they are of course British which I would assume you probably are not (have you heard of the weight of stones as a unit ?).
You are pretty certain to have reached your ultimate body height already and some years from now you will start shrinking, but only by a few centimetres in total regardless of how old you become. I hope you are not dwelling too much on some imagined importance of a centimetre or two - your height is what it is and in your case pretty average overall globally so you should be content that you "fit in" if that is what concerns you.
Released when I was a just a little bit younger than you are now.
Long Tall Sally
Gonna tell Aunt Mary 'bout Uncle John
He claim he has the misery but he's havin' a lot of fun
Oh baby, yeah baby, woo
Havin' me some fun tonight, yeah
Well long, tall Sally
She's built for speed, she got
Everything that Uncle John need, oh baby
Yeah baby, woo baby
Havin' me some fun tonight, yeah
Well, I saw Uncle John with long tall Sally
He saw Aunt Mary comin' and he ducked back in the alley oh baby
Yeah baby, woo baby
Havin' me some fun tonight, yeah, ow
Well, long, tall Sally
She's built for speed, she got
Everything that Uncle John need, oh baby
Yeah baby, woo baby
Havin' me some fun tonight, yeah