Hay, first time mom struggles talaga! Honestly, 37 weeks pa lang kayo so it's possible na mucus plug na, pero hindi automatic na labor agad, some mums in my circle noticed theirs at 37-38 weeks then nag-deliver pa after 2-3 weeks, habang may isa na wala pang obvious plug pero dumating na agad ang labor. The watery or pinkish discharge is normal to watch at this point, pero if it's really stringy and mucus-y or may blood tint, that's more of a tell. Since mataas pa si baby based sa check-up mo last Saturday, baka not quite ready pa siya, so don't panic, but do keep an eye on any sudden changes like water breaking, heavier bleeding, or regular contractions na painful.
Definitely check with your OB ulit if you're unsure, especially since you're so close na! They'll know best based sa actual IE findings nila. Good luck, mama!