Had unprotected sex on the last day of my period been a week and i'm exhausted and feel under the weather is it possible i could be pregnant?

Sure: Can do a preg. test. A urine preg. test gives a reliable result 3 weeks after sex (3 weeks after when conception might have occurred), or 1 week after missing a period. If done sooner, a positive result is likely real, but a negative result may be due to testing too soon, and thus lead to a repeat test. If a woman gets her normal regular period, then she is not pregnant, and a test is not needed.