Is there a minimum degree of illness (subjectively speaking) for which one can request a refuah sheleimah (a speedy recovery) while saying Shemona Esreh? Can one request it for one’s child, for example, if (s)he has a cold? Or one’s spouse, if (s)he has a headache?
I have two thoughts that might help us calibrate
- the definition of a sick person on Shabbat for which we are allowed to take medicine is someone who needs to lay down in bed or if he has a pain that is bothering him and his whole body pains him, even if he still walks, he is similar to someone bedridden (SA OC 328:17) - it stands to reason we can pray for someone like this
- in a related question on MY, I was told "[the addition in] refaenu is meant for urgent/critical cases, e.g., sudden bad news or a hospital operation, and is not meant to be said over long periods of time for chronic cases."
I would therefore suggest the threshold needs, at a minimum, to be enough to call someone sick on shabbat and is meant to be of temporary nature.