呼吸很急促------very formal
喘不过气(来)
or
上气不接下气
there two are different. u can use 喘不过气(来) for all kinds of cases as long as someone breaths very fast or out of breath. he is maybe get hurt, or get sick, or do some sports. we dont know.
however, 上气不接下气 is always used for only one case: do some sports