I have seen ready-made medical bracelets in the USA but not in Taiwan. How about going to the shopping center and buying a bracelet? You can then ask for it to be engraved with whatever text you like. Buy one for each wrist if necessary for more text space. But you would probably have to make a red cross to stick onto the bracelet because your child is too young to show people; in that case your shirt idea is very effective. Maybe you can do both.
Maybe you can print your own? You can buy special thermal transfer paper for clothes. You put the special paper in your printer and print your document or picture to the special paper. Then transfer the image using a standard clothes iron. I have seen many demonstrations in Nova.
Have a photo lab print it for you? If you convert your message to a digital image, you can have any digital photo lab print it onto a T-shirt for you. Just visit a digital developer for more information. The samples are usually hung on the wall.