Should I train after the massage?

You see it’s hardly ever that answers in life are black or white. Most of the time it’s 50 SHADES OF “IT DEPENDS”

It depends on: 
What was the reason you went for a massage? Is it because you feel drained? Exhausted? Your body hurts, your muscles feel tired? You’re having a stressful time in your life? You’re overtrained? (Yes overtraining is a thing but that’s a chat for a different post) In this case the answer is NO! You don’t go back to the gym straight off the massage couch. You go home, make yourself a cup of a herbal tea with honey, put on some candles, sit your ass on the sofa and chill. Give your CNS a break. Let your breath travel to every cell in your body. Then go to bed a get a GOOD NIGHT SLEEP and that’s what we call RECOVERY! You wake up in the morning, feeling as if you got star-dusted by baby unicorn ready to get back on track.
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There’s also scenario number 2! You don’t necessarily fit into scenario 1, you’re just stiff as a board your ROM sucks, you’re half-repping your way through sessions and walking through the valley of injury and mobility of T-rex then the answer is HELL YES! Deep tissue work often combined with PNF stretching will create a new ROM in the joint. Which is exactly what you want! That change will not be long term unless you train your brain to the new setting. Best way to do it? Head to the gym and work in that new ROM under tension. RULES! Go LIGHTER than you normally would. Your muscle doesn’t have the same strength in the new ROM. Build it up.