My T did a little research. Turns out, my new HMO has a transitional care option for patients like me who are in desperate situations and cannot immediately change Ts. The option allows me to see my current T for 60 days and be covered by my new insurance even though my T is not a participant in my new plan. T also advised that it is possible to apply for an indefinite extension past the 60 days in urgent cases like mine. Of course, such an extension would need to be approved by the HMO.

This is really a blessing because i am in really bad shape and needed an emergency appointment. I could not go a week without seeing the T without getting seriously depressed. So, please make a note of it, there is such thing as "transitional care" provisions that will not require you to change Ts even though your insurance provider has changed.