How can I check if time period is already exist or between a specific period in database?

I have this query in my php. What i need to do is. i have example.

8:30 am to 10:00 am. so i want this time start and time end to be checked if it already exist in the database or it is between a time period.

input: 8:30 am to 10:00 am == database: 8:30 am to 10:am. -> already exist

input: 8:30 am to 11:30 am == database: 8:30 am to 10:am. -> already exist between

input: 9:30 am to 11:30 am == database: 8:30 am to 10:am. -> already exist between

input: 7:00 am to 11:30 am == database: 8:30 am to 10:am. -> already exist between

input: 7:00 am to 10:00 am == database: 8:30 am to 10:am. -> already exist between

input: 7:00 am to 9:30 am == database: 8:30 am to 10:am. -> already exist between

the code below works except that if the time start or time end is between the existing periods.. it still continues and doesn't tell me that it is already existing in between a period. i don't know what im lacking. thanks!

$Query = mysqli_query($Connection->con(),"SELECT 
                                          * 
                                          FROM room_schedules 
                                          INNER JOIN rooms
                                          ON room_schedules.Room_ID = rooms.Room_ID
                                          WHERE ((('" . htmlspecialchars($_POST['starts']) . "'
                                          BETWEEN room_schedules.Starts
                                          AND room_schedules.Ends)
                                          AND ('" . htmlspecialchars($_POST['ends']) . "'
                                          BETWEEN room_schedules.Starts
                                          AND room_schedules.Ends))
                                          OR ((room_schedules.Starts
                                          BETWEEN '" . htmlspecialchars($_POST['starts']) . "'
                                          AND '" . htmlspecialchars($_POST['ends']) . "')
                                          AND (room_schedules.Ends
                                          BETWEEN '" . htmlspecialchars($_POST['starts']) . "'
                                          AND '" . htmlspecialchars($_POST['ends']) . "'))))