We appreciate the sensitive nature of this question.
We assume from your question that using an IUD or diaphragm with spermicide would be medically ruled out. If they are not, either one would be a halachically preferred course of action.
We would also recommend discussing with your physician the side effects you are experiencing with hormonal contraception. Symptoms often improve after a few months of use. If they don’t, changing to a different form of hormonal contraceptive can sometimes make a difference. If you’re using progesterone-only contraception, you can discuss with your physician whether and when it might be possible to switch to combined hormonal contraception. Combined hormones can affect milk supply, so this would depend on whether you’re breastfeeding, how well breastfeeding is established, and the age of your baby.
Even among similar types of hormonal contraceptives, a different formulation or delivery method could make a difference in side effects. For example, among combined hormonal contraceptives, the NuvaRing’s hormonal effects tend to be more localized, and thus it might provide you with the contraception that you seek without the negative side effects.
Please see here for further discussion of mood-related side effects of hormonal contraception.
If no other contraceptive options are suitable, then in situations like yours in which pregnancy would be life-threatening, a tubal ligation may be permitted after individual rabbinic consultation. Within the methods of surgically blocking the tubes, there may be some preference to the use of rings or clips, which at least in theory, can be reversed, over actual destruction of the tubes, as in their ligation. Ordinarily, long-term sterilization is prohibited. But the prohibition for men is on a Biblical level and for women it is rabbinic, so a tubal ligation would be permitted before a vasectomy.
Please be in touch to follow up and to let us know if we can be of further assistance.