Noise cancelling headphones don’t work against babies. They are designed for cancelling ambient sound by playing frequencies to cancel out the noise, but can’t predict sudden noises like children crying very well. Earplugs or earbuds do a better job at drowning those out by plugging your ears from outside noises
Without any crime to suspect you of, they might detain you and question you. It’s not uncommon for people to turn themselves in for crimes, and there are legitimate reasons to do so especially with a lawyer, namely to get out on bail easier, avoid having the police raid your home or place of work, and perhaps used to sway the prosecution for a more favorable sentencing, but if the police have no clue what to even charge you for and they can’t figure one out, they’ll just be confused and frustrated, which is a dangerous combination for police