Can I Get Sick From Dead Mice In The Walls?

Erm, yes, of course. The bugs will be trailing all kinds of lovely bacteria all over your place, and you will be picking up the germs on your hands, food and clothes. Do you have a public health authority in your country? If so you need to contact them to come and clear out the mice and bugs. Or your landlord. I don't know what your housing situation is, but you can't live like that, it's unhygienic and potentially dangerous for your health.

Yes you can,knock down the walls and get rid of them dead rats also clean the air in that room with an air cleaner,and clean that room,I hope this works.