I had protected sex with my girlfriend at July 22 and I didn't ejaculate inside but after 2 days there sso many symptoms that she is experiencing right now like Head ache, Dizziness, swollen breast and she always gets tired after work. And niw shenhad her period in the expected date but she didn't experience any menstruation cramps not like for the past periods she had. I just want to ask if her period is due to implantation bleeding or it is just normal to them to have period without having amenstruational cramp?

There is no normal. There are so many variable symptoms of both menstruation and pregnancy that it is IMPOSSIBLE to tell without a test.

Given that she got her period since July 22, chances are, however that she is NOT pregnant, by some reasonable probability. Never 100%.

Sounds to me that she worries a lot, and you might want to consider not having sex until you are both very well read on the subject. That could take a week full time.