Sure, it's possible. People's brain and body chemistries are different, it's totally possible you're just more sensitive to those changes.

I tend to respond immediately to medication like that. I started taking a low dose of Vitamin D to help with depression and felt better almost immediately. Another time, an idiot therapist gave me medication for ADHD, and I was measurably more focused on the first day of the lowest trial dose (though, the effects turned painful as the dose went up and were unbearable by the end of the trial, so much I stopped taking them).

There's also a possibility of a placebo effect - you feel better partially because you're sure it will help you feel better.