Birth Control Options

So, I was diagnosed with idiopathic anaphylactis and my by tracking my cycle my GP thinks the cause may be due to hormonal changes. This started during my second pregnancy with severe urticaria and progressing to anaphylactis postpartum. I'm now 9 months postpartum and after two children I'm done anyways.
I've been warned that another pregnancy could result in anaphylactic shock and hormonal birth control isn't an option. I've been going back and forth between a tubal ligation and a copper IUD. I was hoping to get other women's experiences with both. With tubal ligation how long were you in the hospital? And how long was recovery? Has anyone experienced any serious side effects from a copper IUD or pregnancy with it?