Q. What can be given for fast relief to a small dog who is very constipated?
A. The quickest option is an enema from your vet. At home you can try adding a couple of millilitres of liquid paraffin or lactulose from your pharmacist to the food a couple of times a day but if there is any chance that the dog has eaten something it shouldn't have and may have a blockage this should NOT be done as it can cause serious problems.
Also if the dog is very constipated thus is unlikely to work. I would recommend having an examination by your vet as the safest and quickest treatment.