Pretty close, but I'd say: "I'm drinking an amazing cup of coffee with soy milk. I have a little headache, but I prefer not to take any pills."
Just a few spelling mistakes/typos, plus I also added "cup of" before coffee, since we don't usually say "a coffee" in america (I think they say it in the UK sometimes though). "some amazing coffee" would also be correct.
edit: just noticed you changed it to "I am suffering a little headache"-- you could say "I am suffering from a little headache" but you'd need the "from" there.