Shouta Aizawa, aka Eraserhead, here to keep an eye on a potential threat.

"E-Eraserhead?!" Izuku stammered as the pro-hero entered the room. "Why are you...?"

Izuku could've sworn he saw a flash in the man's eyes before he interrupted. "I'll get to the point quickly, you're under investigation. We know what you did, and roughly why, it wasn't hard to piece together from your research and records. It wasn't illegal, but it was idiotic, and now you're a potential threat. These quirks are usually unstable, and potentially very dangerous, and until we know what yours is, you're under observation." He paused. "You know who I am so you can probably guess why me. Once you're released, you'll be moved to a safehouse away from civilians for a while. You're not under full house arrest, but you're not going anywhere unaccompanied, nor having guests when I'm not nearby. Understood?"

Izuku looked down. "I...Understand. It makes sense." There was a pause. "I just...I wanted..."

"I know what you wanted. This was stupid, and not the way to get into UI. There are plenty of other ways to help the world without a quirk." He scowled. "Someone should be by to have you released into my custody shortly, and I'll take you to your home to get anything you think you'll need. You may be away a while, plan accordingly."

So it was that Izuku found herself living in an isolated cabin in the middle of nowhere. Aizawa mostly left her alone, checking in regularly, but mostly they...Aizawa and whatever government agency had sent him, relied on cameras and a tracker anklet to make sure she didn't try to leave alone.

Which was fortunate, as by the time the arrived, Izuku's cock felt like it was going to literally burst from her throbbing erection, and as soon as Aizawa was gone, she spent a half hour in the bathroom jerking off...thinking of Tsuyu.

She felt a twinge of guilt at fantasizing about her new friend that way but well...she'd been the one to give her her first blowjob, it seemed pretty justified.

After that, Izuku spent a fair portion of every day in the bathroom. If she didn't release at least twice a day, she started getting swollen and couldn't concentrate well, and the bathroom didn't have cameras inside.

She texted Tsuyu back and forth a few times, and even called a few times. There was no progress on discovering any hidden secrets of her quirk for a long while, until right before Christmas, when Tsuyu called her.

"Midoriya-chan, I know you...don't have anyone else there, and I wanted to know if you'd like me to visit, kero." She sword she could hear the frog-girl blushing through the phone. "You shouldn't be alone for Christmas. I can come by after I'm done celebrating with my family, kero."

After a quick check with Eraserhead, Midoriya confirmed that would be great.

And after all, her quirk didn't seem to do anything dangerous so far.