-- or it's harmless planaria.
My plakat gets them on him when he's been hunting through the weeds in his tank. They drop off after a while, disappear.. they eat fish poo and junk at the bottom of the tank and usually aren't seen at all unless there's too much food/waste lying around and a population explosion happens, or there's a major change in the water that drives them out of the substrate. If you've recently medicated your tank, that'd do it.
Could be gill parasites, but if it was that he'd have been sick as a dog long prior to being exposed to ich medication if he's this sick and there's enough flukes, and big enough ones, to be seen crawling all over him..
Did you medicate the tetra? If so, did you do so in the tank (I'm assuming the betta is in the same tank)?..
If it was in the tank, was the betta sick like this -before- the medication? Or did you not medicate the tetra and then the betta got sick, and then you added ich cure?
These details could help figure out what's wrong with him. Please don't panic-medicate, as too much/unecessary/wrong medications can actually cause your fish to become sick...