I use narrow phonetic transcription in my job. The one symbol I need but can't seem to find is a way to mark stretching of the tongue from side to side. Does this exist? I have made up my own, but I'd rather use a standard symbol if possible.
To my knowledge there is no official (or even conventional) symbol to describe that gesture. If I had to pick a symbol to describe "tongue spreading", I might pick
U+20E1: combining left-right arrow above. Here it is on a schwa: ə⃡
I would choose that because
U+034D (combining left-right arrow below) is used in the IPA extension for disordered speech to describe lip spreading, so there's a natural parallel there.
It's not clear what you mean by "stretching the tongue from side to side". You can do that with your fingers (if you have a dry tongue), but otherwise it's not possible -- the tongue doesn't stretch that way. There is no symbol to denote this, since the situation you're describing does not exist. Presumably you mean something else -- we'd have to know what you're referring to.
Based on the comments, it appears that the question is about laminal sounds, which are notated with the diacritic ̻ . Although it is usually added to consonants, nothing in principle prevents using it on a vowel. The Tarama variety of Miyako Ryukyuan is said to have such vowels, and perhaps some Wu varieties of Chinese have them.