Thinning hair/bald patches in young woman. What are my options?

I would suggest starting spironolactone, getting a full hair loss workup with hormonal optimization, starting PRP/acell injections, see link for products at home.... all to avoid transplant for now. you may have a mixed pictures of hormonal and stress related loss.
I suggest a formal consultation as there are a combination of treatments that can be done to improve har loss.  Oral finesteride has very little to no side effects in the majority of people; PRP/platelet-rich plasma + stem cells like A Cell help regrow hair and slow down the thinning process; rogaine and restorsea spray should be used daily; oral viviscal helps keep nutrients high in the follices as well.  Transplantation is a last resort but works early in the aging process as well.  A formal consultation and combination treatment is needed.  Best, Dr. Emer.