Sorry to hear that! (HELP PICTURES BELOW!)
First of all, make sure that you have unlocked and built all three production lines needed to supply all the material required at your hospital. Right next to your distributors' area, you must open these three departments to administrate the right medical material to all your medical rooms. Check if the specific room blocked is asking for medicine (medication supplies), bandages (dressing supplies), or surgery tools (medical instrument supplies). These three areas may require some research. Kindly check the research list out if you don't know how to unlock them!
*IF you have all the production lines unlocked and properly upgraded but you still have blocked rooms, fire all the supply administrators and distributors, and rehire them all.
How your medical administration area should look to succeed:
The three icons for different materials needed to move on:
Medication Supplies
Dressing Supplies
Medical Instrument Supplies