Towers are specific to an airport, so Ohare tower would not control Midway.
If Chicago Approach is online, then I think they would control Midway, and other airports within their airspace. As you approach the airspace as shown on map.vatsim.net, they should send you a “contact me” ping on VPilot (with three quick beeps).
If in doubt, you can tune their frequency and say “Chicago approach, are you controlling approaches to Midway?” Or even sent them a private message in VPilot (right click on their callsign on the left menu).
Here’s a good website someone posted a while back with an interactive section showing the “Top Down” structure of VATSIM:
ATC on VATSIM (dottycomma.com)