The meaning inside would be something like this 'If you wear like that in this weather, 감기 걸려요(you'll catch a cold!)!' If you just say '감기 걸려요.' without any situation, it means 'catch a cold' 'Be careful not to catch a cold.' = '감기(에) 걸리지 않게 조심해요.' which sounds like 'be careful not to caught by cold' though.. anyway, hope it helped!

반말: 따뜻하게 하고 감기 조심해~ 높임말: 따뜻하게 하시고 감기 조심하세요 :)