
Hi
Sorry to hear you're having problems with this little pup.
We have 3 week old puppies here too, so I know how worrying it it when there's one not doing too well.
With our smaller pups (we had 2 smaller than the rest), I would always wait until the milk was flowing (a few minutes after they have started suckling) then pull the of the bigger ones off and put the little one on. You have to hold back the others from barging the little one off the teat - I did this by putting my hands either side. I know you can't necessarily do this for every feed but I know this helped the little ones get their fair share of milk and are now doing really well. I always think mum's milk is best if at all possible.
Are you weaning them yet? This will also give this little one a better chance as there will be more mum's milk to go around.
As for the liquid being brought up, I would imagine that it's probably just some milk coming back up after drinking too quickly. Are you using a bottle or syringing? I was advised a few days ago by knowledgeable people on here that the pups should be able to lap now, so your little ones should be able to lap some milk from a dish. I'd probably rather do this and let this little one have individual time on mum rather than supplement her.
Good luck, I hope all will be well in the end.