头(tóu)一(yì)天(tiān) is the first day of the certain period of time while 前(qián)一(yì)天(tiān) is a day before the reference. For example,
Kǎoshì de tóuyìtiān tā hěn jǐnzhāng
Exam the first day he evaluative marker nervous
He was very nervous during the first day of the exam.
Kǎoshì de qiányìtiān tā hěn jǐnzhāng
Exam a day before he evaluative marker nervous
He was nervous the day before the exam.