Oh dear! I'm so sorry! I hope the poor baby feels better soon. That's so cool that Rex goes to work with you, I wish my babies could come to school with me...
I wonder if you could fix some kind of harness like a belly band around just his tummy that you could attach a leash to take him out. What about a baby onsie with a ring sewn on the back...I'm not real crafty - I'll bet someone on yt has an idea. I hate for him to be away from his mommy when he feels badly.
Best wishes for a speedie recovery!