that's all good! @Snowie
i know those are some really painful and hard words to admit to a loved one. and i can imagine the guilt you must feel when you think about how it impacts your family. i can't promise you that those words won't be hard for him to hear, but once he's had a chance to process it, he can support you much better after he knows the truth.
let's think back to why your psych wants you to tell him in the first place - she wants to help reduce your SI and SH, right? so she encourages you to tell H so he can listen and support you during those tough times. and if he fully aware of what's been going on for you, you can continue to lean on him and those thoughts you mentioned may not be as intense, or perhaps a lil easier to overcome.
you both deserve to have that honest communication between each other. you both are allowed to lean on each other. it's okay to be honest with him, and from what you've mentioned about H so far, he seems like he'd take the time to understand.
