early labor?

S
35 weeks 5 days.  It's 4:33 am.  My lower back is so painful and uterus kinda gets tight.  It's gotten tight a few times over the last few hours but the last one REALLY HURT.  I'm trying to time it with a contractions app.  I've had BH before... doesn't quite feel the same.        We had sex (amazing intimate 🤤) around midnight.    
Umm possibly early labor? 
Update question: am i correct that if I was full term I would just ride out labor symptoms at home but if I was preterm come in once I suspect that I'm in labor?? 
UPDATE: went to the obgyn around 11.  I am 2 cm dialated and they were legit Contractions because I had one at the office.  But because they weren't anywhere near as intense I'm not in labor.  The back pain is due to the baby dropping and putting pressure on my lower back.  So she's in position!  But this could still go in for a few weeks.  She expects me to make it till 38 weeks. All is well,  things are happening just not all happening at once.  I'm right where I should be :)