Can I sue the County Jail for not treating my fiance for a wound?

The answer is it depends.  I know that isn't quite the answer you were looking for, but in these types of cases it simply depends on all of the details.  Now, what you will need to keep in mind is that to prevail in a case where you are claiming that the county jail has denied your fiance medical treatment, your fiance would have to be able to show that the county jail (and specifically the individual jailers responsible for providing him with medical care) were deliberately indifferent to his "serious medical needs."  As the courts have explained, this is in essence a two part test.  First, were the jailers aware of a serious risk to the health of your fiance and if they were aware of this risk, did they ignore it.  The other issue is what qualifies as a "serious medical need?"  Basically, this is anything that a doctor has prescribed treatment for or that any lay person would know needed treatment.     One other thing to keep in mind is that an inmate's civil rights are not typically violated if there is a disagreement regarding the treatment he should be receiving.  So, for example, if they have given him some medication (like ointments or antibiotics), but he thinks they should be doing something more or different then the court would probably determine that his civil rights were not violated and side with the jail.