Thank you for the extra info. You're right to be concerned, but your and your daughter's observations have served this bird well for him to be 14 years old, so once again, good job.
Let me go over a few different things it might be - and then you proceed from there based on what your instincts tell you. You know your bird and you know in your heart what's serious.
A bird that bobs its head up and down in a sort of pumping motion, beak open and then a purposeful delivery of partially digested food is regurgitating. This is something they would do to feed offspring or a mate. It’s done by some birds to objects they are particularly fond of, especially if they’re in a breeding season.
It might also be done when the bird is nervous or trying to ‘please’ you.
Regurgitation that is unusual enough for you to make note of it like you have, might be a symptom of crop infection or other problems; and it’s a threat because it can lead to malnourishment. If your bird is giving up too much of the food they should be digesting for their own nutrition, the result can be pretty serious.
Vomiting is more of a head ‘flicking’ event. The bird will often seem uneasy, pacing or uncomfortable and although the head bobbing might be similar to the regurgitation action, it’s usually more of a shaking and the end result is a very splattered, sticky substance that may or may not include food.
If possible, collect a sample of this substance to bring to the vet with you.
When there’s a blood showing in the vomitus it may indicate esophageal or proventricular ulcers (http://www.multiscope.com/hotspot/pdd.htm) .
The vet will take a look into your bird’s mouth for other symptoms and I’d ask for a swab culture if the vet isn’t going to do one anyway. A good exam will also check for any growths or tumors.
Vomiting is a more serious symptom and seeing a vet as soon as possible is important.
There are far too many possible diseases to outline here, but as in any case of illness, getting it evaluated, diagnosed and treated right away is often the best outcome at the lowest cost.
The top causes of vomiting in domestic birds are (gram-negative) bacteria, something that may increase to a troublesome point after the bird is stressed somehow.
Stress can involve changes in their environment, being frightened, having their sleep hours reduced or other changes in schedules or even a difference in food.
The other possible causes are contamination of food or water by fecal matter. Did he maybe leave a dropping in something he later ate? Even if it's happened a hundred times before, lack of complications from it might have been just plain lucky.
Candida (also increased after a stressor) infection or Trichomonas are also causes that should be explored by your vet. When these are all ruled out, the search for a cause can get pretty complicated.
Cockatiels and other companion birds are known to contract Bacterial Enteritis
– caused by salmonella, E.coli, coliforms and other bacteria infecting the intestinal tract.
The reason I'd suggest having this little man seen is because some of the potential problems could be zoonotic, putting you, other humans and even other pets at risk of infection.
If your bird will drink and eat on their own, excellent. If not, have an eyedropper ready to administer a few drops of plain water, or better yet, children’s Pedialyte every 20-30 minutes. Put the dropper gently inside the beak and let the drops fall into the bottom beak under the tongue rather than trying to get into the back of the throat. We don’t want to chance the bird inhaling the fluid and developing pneumonia.
Another feeding option is to offer ½ spoon of all natural, organic baby food (squash, yams, sweet potatoes, mixed vegetables) which many birds take readily; also try some pabulum or baby rice cereal and a few licks of natural (no artificial anything) yogurt.
You can see how he does with this - but if you don't see an improvement in 12-24 hours, I really wouldn't wait.
Of course if you see any worsening, that's important too - no waiting.
Please let me know how you make out ok? 'tiels are one of my soft spots. One of the best birds there is!