Twice already I burnt a hole trough my silk dresses. People say to iron silk you need to do it in low heat inside out.
I always iron inside out any garment. It comes out nicer. Silk is one of the most durable fabrics. I would use low heat, and if you are apprehensive, put a cotton towel between the iron and the fabric.
I had the exact same problem during my pregnancy, I was prescribed iron tablets and vitamin b12 tablets (to help my body absorb the iron tablets). This did not alter my iron levels when they were tested, but I did feel like I had a little more energy. My baby was early but suffered no effects from my aneamia. I did end up staying in hospital for 6 days though because of the blood I lost during labour, and already being aneamic meant my levels were really low, and I did feel faint a few times so prehaps pack more than if you were going to stay just over night. Good luck and try not to worry!
Most irons have a silk setting. Use a pressing cloth if you are nervous about it ( a dampened piece of muslin, pillow case, etc ). Lay the pressing cloth over the silk item and iron over top the pressing cloth. It is probably best to iron silk on the wrong side to avoid any shininess that might develop in the ironing process from showing.