Cold sore
You cannot give blood with an active cold sore if it is your first ever cold sore. You must wait until you are well and have no symptoms and the cold sore is fully healed.
If you had a cold sore in the past and you have a cold sore now, you can give blood as long as you are well and if the sores are healing (i.e. scabbing over and there is no tingling) and there is no infection (signs of which may include redness and / or oozing).