In your language, what is the sound when you sneeze "Achoo !'' and when you cough "Cough cough !''
In Turkish: Hapşu ! and Öhö öhö !
Polish: for sneezing it's "apsik" or "aaapsik!" for a longer sneeze. There's no singular sound for coughing, but it would be something like "ehym, ehym" or "yhy, yhy", like for clearing one's throat.
There's a lot more of curious onomatopoeia expressions:
"ziuuu" for the sound of throwing something or speeding by, "chrrrr" for snoring, "trzask" for slamming or clashing and crackling fire, "puk, puk" for knocking, "człap, człap" for stomping heavily, "chrup, chrup" for crunching, "dzyń, dzyń" for ringing a bell, "dryń, dryń" - phone rings, "ćwir" for chirping, "kap, kap" - dripping water, "plum" or "chlup" as something falls into water, "ciach" for cutting, "ciii" for "pssst", "bach" as something falls to the ground, "pac" for patting, "mniam, mniam" for "nom, nom", "pstryk" - sound of taking a photo, "cmok" for kiss sound, "brzdęk" when ie. a metal bowl hits the ground or glass breaks, "stuk, stuk" for knocking also, "skrzyp" for creeking, " bul, bul" for boiling water or bubbles in the water ;D
Come to think of it, they probably look a bit weird to non-speakers ;P there's a lot of "sh", "ch", "dz" sounds, it's kind of rustling.
In Portuguese that would be "Atchim" for sneeze and "Coff coff" for cough.
Filipino: If you're referring to the sneeze itself, the term is "bàhìng" and "ùbo" for cough. But if you refer to the sound itself, sneeze is like (note: letters and phonemes in  are sometimes included and sometimes not, it won't matter) "[h]atchu", however, the sound of cough, violates a Filipino ortographic rule: a circumflex couldn't be placed anywhere except to the last letter and if that last letter is a vowel, Filipino cough sound like 3xhe (without phlegm, to be exact) and êhe (with pleghm, to be exact)
The 3 is like the /eayn/ sound in Arabic, I couldn't put an accent on numbers, there should be a macron or an acute there, depending on the region, some dialects differ in sound, but that's what they all have in common. In Tagbanwan (Palawan dialect), I have heard my uncles (native Palaweños) sneeze like hwàtchu. Also the cough with pleghm might go a little step further, sometimes, there's some sort of ö sound alongside ê, making an hx or an üx sound somewhere. Yeah, Filipino ortography is weird, we don't even have an umlaut.
P.S: The 3 is the closest possible phoneme for that 3xhe