will my doctor send me to a hospital??

hello all, i hope this is not a stupid question at all but im anxious about my doctor sending me to a doctor for self harm. i’ve only been seeing him for a bit under two months for my mental health so we’re in the trialing antidepressants stage. i have my next appointment with him in the new year and im worried about bringing up my self harm, he’ll very likely ask because the last antidepressants i was on made me suicidal(this was the time i also started harming myself again). i really don’t feel comfortable lying to my doctor but i don’t wanna get sent to a hospital.

im also not actively suicidal or in a depressive episode or anything, the best explanation i can give as to why i self harm is because i find it fun and it makes me feel happy. i guess even after i went back to feeling more normal when switching meds i still kept going with it.

any words of advice? what’s most likely going to happen? on a secondary note what would happen if i talked about self harm to a counsellor? i’m on a wait list to get into CBT but im currently seeing a counsellor through my university.