Use 'check into' when you are mentioning the time you plan to report your arrival.

Arrival Time

'Check into' is used for arrivals, unlike 'check out' which is used when leaving.

Not For Departures

'Check into' often relates to travel situations, like in hotels or airports.

Use it to mean beginning an investigation or inquiry into something.

It can imply an initial suspicion that leads to an investigation.

'Check into' does not imply a decision or conclusion has been made.

Use it to refer to the process of being admitted for medical care or treatment.

It can denote a planned admission, not only emergencies.