First of all I hope you never need to use these words, but since you can’t decide when and where to get sick or hurt, it’s better to be safe than sorry.

• medicine (the field): طِب (ṭib) or عِلم الطِب (ʿilm al-ṭib, “the science of medicine”)
  
• medicine (medication): دَواء (dawāʾ), plural أدوية (adwīyah)
  
• doctor: طَبيب (ṭabīb), دكتور (duktūr, title), حَكيم (ḥakīm, “wise man,” kind of archaic)
  
• nurse: مُمَرِض (mumarriḍ)
  
• hospital: مُستَشفى (mustashfá)
  
• ill (adjective): مَريض (marīḍ)
  
• illness: مَرَض (maraḍ)
  
• injury: جُرح (jurḥ)
• injured: مَجروح (majrūḥ)
  
• “I am ill”: أنا مَريض (anā marīḍ)
  
• “I am injured”: أنا مَجروح (anā majrūḥ) or أنا مُصاب (anā muṣāb, “I am a casualty”)
  
• “Where is the hospital?”: أين هو المُستَشفى؟ (ayna huwa mustashfá?)
  
• “I need a doctor”: أحتاج طبيب (aḥtāj ṭabīb)