That sounds a lot like me and my bf. Good for you two, working on being honest! I think that's really important in relationships and being able to say what you are thinking and feeling is the only way to really know each other.
Telling my bf about my SI was really hard (I cut) and it was realy awkward at first. Sometimes it still it is. I know he doesn't really understand why I do it, just that I hurt myself and it upsets and hurts him to. Having someone else know and care about what you are doing to yourself makes it a lot harder to just say "What the hell?" and give up and give in. Which is a blessing and a curse in my case.
If you are still having urges, I think that it might be something to share with your bf. Not in too much detail, just the facts. SI is really hard for other people to understand. Just let him know that it is something you sometimes struggle with. If he cares about you, he should respond well. Talk it out until he understands what you are saying.
That's just my two cents (and its called 'two cents' for a reason- it ain't much!

) and I wish you all the best, whatever you decide to do.