Aww mama, nakakapraning talaga ang first labor signs, di ba! Ang Braxton Hicks contractions ay normal sa 37 weeks pa lang, they can get more frequent and stronger as you get closer, pero hindi pa ito siyam sure sign na labor na. The white discharge you're describing sounds normal din, kaya wag mag-alala doon. That said, since you're noticing the contractions are getting a bit more painful even though they're mild, it's best to check in with your OB just to be safe and get peace of mind, a few of us mums went in for checkups around this time and it really helped us know kung we're on track or if we need to be monitored. Hang in there, you're almost there na!