27 "days"
We can establish this from Picard's logs; Worf's injury occurs on stardate 45587.3:
Picard: Captain's log, stardate 45587.3. Lieutenant Worf has been removed from active duty following a severe injury. Although a neuro-specialist has arrived, Doctor Crusher believes his paralysis may be permanent.
Star Trek: The Next Generation Season 5 Episode 16:"Ethics"
And "The Outcast" opens on 45614.6:
Picard: Captain's log, stardate 45614.6. We have been contacted by an androgynous race called the J'naii to investigate the mysterious disappearance of one of their shuttlecraft.
Star Trek: The Next Generation Season 5 Episode 17:"The Outcast"
According to a guide on translating stardates, by 1992 (season 5), they followed a specific format:
A Stardate is a five-digit number followed by a decimal point and one more digit. Example: "46254.7". The first two digits of the Stardate are "46." The 4 stands for the 24th Century, the 6 indicates sixth season. The following three digits will progress consecutively during the course of the season from 000 to 999. The digit following the decimal point counts tenths of a day. Stardate 45254.4, therefore, represents the noon hour on the 254th "day" of the fifth season.
So there are 27 "days"27 "days" between the two episodes. Considering the speed with which he recovers following Dr. Russell's surgery, coupled with Worf's Klingon stubbornness, this doesn't seem an unreasonable recovery period.
If we assume that one season comprises 365 calendar days (an admittedly dubious assumption), then there are about 10 calendar days between the two episodes. This is perhaps straining credulity a bit, but then Worf's alien physiology must count for something.