You could either add the word "and" following the comma or replace it with a full stop. So it would be "My name is Kristina, and I was born..." OR "My name is Kristina. I was born...".
When saying the date it is common to add "of" but this is never written. The correct version would be "7th July, 1990..." If you want to take the American approach then you would just swap the day and month around.