Head held high for sure. In fact, you may have people approach you quietly about what issues they or their family / friends may have with too much drinking. I only told my boss what happened (he was supportive and told me he himself drinks too much), but somehow others found out. The fact that you have gone through that and come out the other side will be seen by many as amazing strength. As to the rumormill, nothing you can do about that, so just hold your head high then too!
I also started back to work after recovery in late 2014. As luck, fate or the Gods would have it, my inpatient stay happened during the time I was off for Christmas (2 week break from work). When I went back I knew I was in a different place mentally...one without daily booze...and this gave me pause to be patient and kind to myself. Went in thinking my job ability would stink for a while, but actually was able to focus better and be more productive not too long after being in the hospital.