I'm sorry to hear that Oliver is ill. I haven't been following your story, so don't know how long you've had him. But give it time. He may (as Ladymom said) just have a sensitive tummy and it might just be a matter of figuring out what bothers him. She gave you great advice about the blood panel, I'd check with the rescue.
I want to take a moment to thank you for taking on this rescue baby. I don't know how long he's been with you, but I know its not uncommon for rescue moms to worry if they did the right thing. You did. Right now you are giving him love and kindness and you are making certain the right thing is done for him. That's all anyone would expect.
Don't worry about having to turn him back into rescue at this point. Cross that bridge if and when you come to it.
Hugs and prayers are being sent your way. Hang in there, and give him an extra hug from me.