Assuming you qualify for FMLA leave (see criteria here:
http://www.dol.gov/whd/regs/compliance/whdfs28.pdf) file a claim. Your job will protected for up to 3 months (unpaid) as long as you seek treatment for your alcoholism (i.e., rehab).
Short-term disability is insurance based. Not all companies offer it. But if yours does, take advantage of it because you may get all, or at least a portion of your salary while you are out.