You have nothing to apologize for. First of all, live and learn, right? Second, many, many, many of us learn things about technology only after our kids come across something we'd rather them not see. I'm the idiot mom who downloaded a game onto the IPad (because my 9 year old asked) that was rated 18+. I didn't even see the rating until several months later when he asked me to download an update. Ug!
Youtube is a huge challenge because once a video is completed, another one loads. If you are not standing right there to monitor, you might miss it. The video that loads next is usually based on your previous browsing. ie, what kids of videos to you tend to watch? Because I've watched videos about the Star Wars movie, Gilmore Girls, Harry Potter ajnd The Hunger Games, those are the videos that are more likely to load next. My boys have watched videos about Minecraft, so those are also likely to load.
I'm sure there are parental settings, but I haven't explored them at all. I rarely let them watch youtube for many reasons, so when they are allowed, they are very highly monitored.
Honestly, I don't think youtube is to blame for your situation. I think your daughter is just going through an "extra needy" phase. When pressed for an answer, kids will come up with something, whether it's strongly related or not. She might honestly have those fears now and then, but I doubt that's really the problem. I also don't think even she really knows why she's being extra clingy. Kids just are sometimes.
Here's what I would do. I would hang in there!!! I would schedule some alone time for myself ... use my husband or my parents or my brother or a sitter. But I would take a night off or an afternoon off. But show her as much extra love and attention as you can. Right now, that's probably going to be the most helpful thing that you can do. If she feels that you are showing her lots of love and attention, she will begin to feel more secure and will slowing stop being so clingy.
I think lots of extra cuddles and mommy love will go a long way!