Worried out of my mind for being overdue!!

Ok so this is my first time ever posting but I’m super worried about being over due with my first son. I’m 40 weeks and 4 days and the ob says my cervix has thinned out and I’ve been 1 cm for two weeks. And I get hip and back pains and tightness but nothing ever happens. The ob is suggesting I look into induction cause they don’t want me passing 41 weeks cause my baby also has xxy and they don’t know if it will stress him out or if it will stress him out just being in there too long because at 42 weeks the placenta starts get old and not let enough oxygen in. I’m super scared and idk what to do because I talk with my bf who is the dad and he says to wait it out but I’m scared my baby won’t make it if I wait so long and don’t do an induction plus I really want to see my baby that I start crying cause I’m so sad he isn’t here yet that every day coming and I feels pains I don’t even think about it no more because I’ve lost hope. I just think about waiting till my water breaks or I bleed. Can someone please let me know what’s best to do please l!?!?