Mercer s disease, also known as MRSA (Methicillin resistant Staphylococcus Aureus) is a highly contagious disease. It is spread mainly by skin contact. However, since you had no skin-to-skin contact with him and you also took protective measures like showering, sanitizing your hands, it is highly unlikely that you could have got the disease. It usually starts as a rash and gets worsened. In order to fully confirm that you have got the disease, I would recommend you to get a few investigations like the culture and sensitivity test and PCR test which will identify it and consult the doctor with these reports. You can also take a few preventive measures such as:

a) Using a mask, gloves while going to visit your brother.

b) You should always sanitize your hands before contact with your brother.

c) If the tests are positive, you can use an antibiotic such as vancomycin that is highly effective against MRSA.

If you have any further queries you can write back to me.