Am I going into labor ?

Sounds like labor

I would go into hospital, if I were you

Can you walk and talk through a contraction? I just gave birth this week at 38+3 and it started off as crampy diarrhea like contractions 5-20 min apart for hours. I was able to talk thru them and continue to do normal things. That lasted 14 hours and then I had 8 hours of 5 minutes apart where I couldn’t walk thru them. I could have gone to the hospital but I waited and was 5 cm when I got to the hospital. My doula advised me to wait until I had lost my mucus plug of water broke but that won’t always happen on its own. And it didn’t I just went to the hospital after I could not take it any longer. I was also afraid that i would be turned away but listen to your body first and foremost!! You got this!!

That sounds exactly like how my labor started and I was also 37w2d