Congratulations on adopting a new member of your family. I am sorry to hear your Terrier had complications after his neuter surgery. Typically, neuter surgeries go really well, so I am really sorry to hear your experience is not starting off all that well.
This is something that you would want to talk to your Veterinarian about.
However, something you mentioned caught my attention. You mentioned that he was in a lot of pain, and when you put him on the grass he runs up to you to be picked up. Why do you think he is in a lot of pain? Normally when dogs are in pain they are not going to be running, and jumping up on you to be picked up. I am wondering if it is more that he is scared? Sometimes a new place, new surroundings can be scary for a dog and they don't want to go potty they just want to be in a safe place, which happens to be in your arms. (especially if you have been caring him around since adopting him) You are his safe zone, where he feels comfortable. I would recommend when you do put him in the grass, try to ignore him a little bit, turning your back to him, not picking him up right away. Encouraging him to sniff a little, letting him know that its okay, he's okay. (a grassy area where other dogs have already urinated in will also help him to want to urinate as well.) I would try that approach and see how he does.
Also make sure you are giving him his pain medication and antibiotics as prescribed. Keeping his mouth off of his surgery site. Signs that you are looking for that your pet is in pain would be not eating, not drinking, slow, doesn't want to get up or really move around, cries in pain, yelping, lethargic, ect. (Running and Jumping on you would not really be signs of pain. )
*Following up with Veterinarian would be highly recommended. *
Best of luck and congratulations again!