Any health effects were too small to be noticed.
According to this NASA article, the gamma ray burst lasted a few minutes with a peak that lasted 0.1 seconds. That peak was huge, containing all the energy the sun would produce in 100,000 years. It was far brighter than the second brightest short burst.
It was also very close as gamma ray bursts go. Bursts are extremely rare, typically a few per million years in a galaxy. But space is huge. There are enough galaxies that hundreds of bursts a year can be detected. Most are from extremely distant galaxies, and are so faint they are only noticeable to sensitive instruments in space designed to detect them. This was from the far side of our galaxy, "only" 50,000 light years away.
So the peak power outdid the sun by a factor of $3 * 10^{13}$. The distance was $3*10^{9}$ times farther than the sun. The upshot is the intensity was $3*10^{-6}$ as bright as the sun. However this was gamma rays. In the gamma ray spectrum, the burst was brighter than the sun. Gamma ray detectors in space were saturated. There were strong effects in the upper atmosphere.
Earth's atmosphere does a really good job of shielding us from the primary gamma radiation. However gamma rays excite UV radiation that does reach the surface. But it was faint, not nearly strong enough to cause, say, a suntan.
Any long term health effects would be from damage to the atmosphere. Gamma rays ionize molecules. Models show this produces nitrogen oxide and nitrogen dioxide. This can deplete ozone, create photochemical smog, and cause acid rain. Smog could darken the sky, reducing photosynthesis and causing global cooling. If bad enough, it would take years to recover.
In this case, ionization was significant down to an altitude of 20 km, just above where commercial airlines fly. At 60 km, ionization changed from 0.1 free electrons per cubic foot to 10,000. It took an hour for ionization to recover.
The disruption of the ionosphere was enough interfere with communications. The ionosphere is the highest part of the atmosphere, nearly vacuum. Radiation ionizes molecules, and air is so thin that it takes a long time to recombine. Ions are conductive, so radio waves are reflected. The ionosphere forms a wave guide. This can be used to talk over the horizon. When the burst ionized the atmosphere down to 20 km, the wave guide changed.
Here are a few links - A Gamma-ray burst Wikipedia article talks about bursters in general. The difference between long and short bursts. Potential effects of life on Earth. Possibilities that Ordovician-Silurian extinctions 450 million years ago might fit the profile of a gamma ray burst.
SGR 1806-20 is a short Wikipedia article on the neutron star where the burst originated. Neutron stars can have immensely strong magnetic fields. This star has the strongest - $10^{11}$ Tesla, 1000 times stronger than a typical neutron star. Compare it to a strong superconducting magnet with 10 Tesla.
Big gamma-ray flare from star disturbs Earth's ionosphere is an article from Stanford Digest on the effects of this burst.