Sorry for the wall of text, I'll try sum it up at the end. But basically yes I do and below is how I handled it.
I had a similar kind of feeling after a 2 year relationship progressed from emotionally to sexually abusive, but I decided I didn't need to tell other people and be believed to know what happened in my head. I also didn't want to, as it would hurt my family and I didn't want to lose my identity to be 'that girl who was raped by her ex' to my peers. So I didn't report it. And just as you said...I was worried I wouldn't be believed. As I already had so much trouble coming to terms with what had happened, facing any of that scrutiny would have made things a lot, lot worse. I don't regret my decision and keep to it now, but keeping it bottled up makes scars too. There will not be much of a support system if you can't tell anyone. Now, a few years later, I've told my current partner, and it's made those horrible re-living periods much easier. I've sought counselling this year, and it has really helping. Better late than never and all that...
Do NOT be worried about your giggling reaction. When I first started talking with my counselor about it, even though it was hurting so much inside to talk about it I could only express myself as extremely stoic as if nothing happened/I didn't care. I even laughed at myself in the way I was describing it, made sneering jokes even. This is NORMAL. There is no "perfect victim". Your head is coping with some very terrible things and as someone who hates being seen as weak that ended up being how I approached it with others. If I'm completely on my own, I am a wreck. You will want to break through this defensive state in your counselling, but do not be embarrassed about it initially. It's normal.
Tl;Dr: don't tell if you don't want to, choose wisely if you do. Definitely pursue counselling - don't worry about 'incorrect reactions' such as giggling or smiling about it - that is very normal and just your body's coping system. Yes others feel the same way about telling people, especially when time has passed and they didn't report it. But see first bit again - you can still tell if you want, or don't if it'll make you feel worse.