Can you feel like or pregnant only 2-3 days after unprotected sex or could it be me wanting us to conceive?

No. It takes about a week for a fertilized egg to implant. Only then does your pregnancy hormone start to rise, initiating early pregnancy symptoms such as breast tenderness.
Sounds a bit early. At 2-3 days after having sex, a woman can feel pregnant but that's so early that it is probably her own mind playing tricks on her. At 1 week after having sex, if the woman is super-sensitive to little changes in her body, she might truly feel pregnant. In reality, none of this is important because the days pass so quickly, and she will know in another few days when she misses her period.