"Uchi" can be used, but the general is only in Kansai area as famous dialect,https://en.wikipedia.org/wiki/Kansai_dialect
it is not used in the whole of Japan as "一人称(ich-nin-syou)".
However, any Japanese knows it, and even if a foreign girl/woman uses it, no one no care.
Basically among Japanese "Uchi" has no element of saying "cute".
If so most girl/woman uses it whole of Japan long years, but did not happen.
And, about "using their own name is cute but a bit so much childish!" is mostly agree,
but we think main reason is quite different(most Japanese dislike) as Japanese.
In most cases, it strongly impresses a "selfish woman".
It is also disliked that Japanese use higher-ranking honorific for handle names.
(ex -sama/Mr. Mrs, -ou/king, -syougun/general, -hakase/Dr. -daijin/minister)
If a foreigner does the same thing, no one cares, but it is only suspected as "2nd year of junior high(14 yd) sickness".
(Maybe you may have heard/seen the word "中ニ病:chuuni-byou". )https://en.wikipedia.org/wiki/Glossary_of_anime_and_manga
Your handle name "Choco-hime" is also same.
We(Japanese) know in many countries making yourself look bigger is not special,
but in Japan that has incorporated a lot of Buddhism moral ideas it is hard to accept.