Is he able to hold down any food or vomiting it all up?
Is he eating anything?
If he is unable to hold down food and even worse not eating, then the best thing is going to be to take him to your local vet now and have him examined. They will most likely recommend radiographs or an ultrasound to further evaluate his abdomen to see if anything appears to be stuck in his intestines causing an obstruction or even worse perforated his intestines. Radiographs will be cheaper but the wood itself is unlikely to be visible on the radiograph but they might be able to see other signs that suggest a problems (gas dilation of the intestines, etc). Ultrasound is typically more expensive but is also more likely to find wood stuck in his intestines or a perforation.
Let me know if you have any further questions.
If you are unwilling/able to take him to a vet at this time, which is the best thing to do, then here are some other things you may try:
A few things you can try at home - you should remove food and water for 12-24 hours. This gives the stomach and intestines some time to 'calm down'.
If the vomiting stops then you can try the below steps, iif not then you should take your pet to your local vet or ER clinic for further tests and treatments.
1) Once the vomiting has stopped, then you should feed a bland food in small amounts frequently. One option is a veterinary prescription bland diet called Hill's I/D or Iams Low Residue.
The second option would be a home-cooked bland diet. A common bland diet is boiled white rice and either boiled chicken, hamburger or turkey. Make sure it is boiled to get rid of any skin, fat, and bones that might be present. Offer the meat with mixture of boiled rice - 1/3 meat and 2/3 rice.Initially only offer small amounts at a time -one bite every 2-3 hoursand as long as doing well then slowly increase the amount of food. Similarly, only offer your pet small amounts of water every few hours (so they don't gorge and puke after drinking too much).
If the diet is tolerated, and once clinical improvement is seen, it is recommended to SLOWLY transition back to the normal diet over 3-5 days
2) Famotidine (Pepcid A/C) 10mg tablets - the dose is 5mg for every 15 pounds of body weight every 24 hours. You can give this daily for 7 days.
3) You can also give pepto bismal. Give 1 tablespoon for every 30 pounds of body weight every 8 hours.
I cannot stress enough that if this is not getting better, or you are noticing loss of appetite, lethargy, continued vomiting, worse signs of discomfort, or blood in the stool, then those would be indications to see your veterinarian for evaluation.
I hope this information helps! If you have any further questions, please feel free to let me know...