Mild cramping along with left-sided and central abdominal pain after a double IUI is common. It usually comes from the procedure itself, the catheter passing through your cervix, and the follicles that released their eggs on both sides. The mild back pain you're describing often goes along with this. The progesterone your doctor started also commonly causes mild cramping and bloating on its own, so this combination fits a normal post-IUI picture rather than anything urgent.
Next Steps
Continue the progesterone exactly as your doctor prescribed it. Rest, avoid strenuous activity for a couple of days, and a warm compress on your lower abdomen can ease the cramping.
Health Tips
Since follicles developed on both sides, go back to your fertility specialist the same day if the pain turns sharp and one-sided, your abdomen swells noticeably, or your urine output drops, since these can point to ovarian hyperstimulation.