Buying drill bits can be hazardous. There are so many levels of quality out there, and good stuff is expensive.
There are at least five bit materials: Carbon steel, the cheapest stuff. High-speed steel, which has more carbon and other alloying metals in it. Cobalt steel, which is HSS with cobalt added for hot hardness. There are the TiN-coated bits, the yellow ones, plated with titanium carbonitride. That's a hard coating that makes the cutting easier and acts as a friction-reducer. Sharpening that bit removes the TiN from the cutting edge. And then there are the solid carbide bits, much more money, but can cut under high heat. They also chip easily, and if you use coolant you have to flood them or leave them dry. Anything in between causes thermal shocks that crack and fail the bit.
I sharpen my bits by hand, even some tiny ones, but if you don't get both flutes right at the same angle, and the chisel edge right exactly in the center, it will drill an oversize hole. Too much rake leaves the cutting edge too thin and it overheats. Too little and the heel drags.
Never used a Drill Doctor. Had a chance to buy one real cheap many years ago, and should have. I have sharpened, by hand, bits from #40 (not much success most of the time) up to 1-1/2" or so. Big ones are easy.
Lots of stuff on the internet as to how to do it. Stuff like this:
Thinning the web, if done right, will make a bit drill like mad and will generate a lot less heat. he idea is to shorten the length of the chisel edge.
Or:
I have also re-heat-treated bits that have been overtemped. Sharpen them first, then heat the end to a dull red and quench it in water or oil. Clean off
all the oxide, then heat very gently until a straw-colored oxide appears, and let it cool. Then give it a final sharpening. Big expensive bits are worth this. Not the average smaller cheap hardware-store stuff.
New bits that chip easily haven't been tempered enough. They're too hard. Do the gentle heating to get the yellow oxide, and they'll work better.