I have a broken toenail & am running into some major annoyances.?

I had a minor accident... I rammed my toe into a chair over the weekend, which broke the nail in the middle. It hurt & bled that day & was kinda sore the next. It felt fine the day after, so no problem I was hoping. However after ramming it hard again (cuz it's kinda hard not to), it affected the rest that was still attached. Now the whole nail is sticking straight up, like a bloody puppet (literally)! It's not bleeding too badly now, just drains if I walk on it too much. Needless to say it looks gross, it's kind of embarrassing, uncomfortable to put pants on, & I can only wear flip flops with latches that I can swing open. If I press down on the it, it's very sore. I'm trying to keep it clean, putting peroxide, neosporin, etc. But I don't even know how I should cover it cuz I put gauze on it yesterday, only for it to get stuck! What should I do, wait for it to fall off, or is there a way to expedite the time to fall off? How long to grow back, risk of infection, etc? Help