Normally when you're positive, you are already about 1 mth plus. No way you're 3 weeks pregnant cos your hcg level is not even high at that time. Cramps are normal during the early stages. Feels like menses cramp but should not be accompanied with bleeding or clots. Book your gynae's appt now. It will take 4 weeks to secure one if you're planning to go to the subsidized route or call/walk in to your preferred hospital.
Normal, backaches and cramps are normal. Because your uterus is preparing to expend, which is ur pelvis area, but do check and mention it to your gynae during your checkup.