I was thinking of "sexual exhaustion", but it's not "sexual exhaustion" since you are not feeling exhausted after orgasm. Your sexual organs just get really sensitive. Is there a word or a term for this? I know it's a weird question, but to this day I have no idea if it has a word or a term.
Although not a commonly used term, it's called the "refractory period",.
In human sexuality, the refractory period is usually the recovery phase after orgasm during which it is physiologically impossible for a man to have additional orgasms. This phase begins immediately after ejaculation and lasts until the excitement phase of the human sexual response cycle begins anew with low level response. Although it is generally reported that women do not experience a refractory period and can thus experience an additional orgasm (or multiple orgasms) soon after the first one, some sources state that both men and women experience a refractory period because women may also experience a moment after orgasm in which further sexual stimulation does not produce excitement.