I gave my 9.5 mo old tylenol (acetaminophen) for teething and within 2 min he threw up his whole breakfast. Should I redose or wait the 4-6 hours?

Try something else. I usually recommend a topical anesthetic applied with a qtip or ice rubbed on area if nothing else available.
Cautious. Give the baby a cold pacifier to soothe the babys pain. If the medicin is over a year old, throw it away. The baby may have consumed some tylenol (acetaminophen) so wait. Do not give the baby sour food. Taste it before you give it to the baby to make sure it is good.Make sure pacifier is ortho approved.
Change the treatment. Your child's teeth are erupting in succession in pairs and at this age a new set of teeth are erupting. The children feel this pressure of the erupting tooth pushing through the gum and it hurts. If you look in their mouth you might even see a taught or swollen area right behind the last tooth in the mouth underneath which there is a new tooth waiting to erupt. The hydrostatic pressure of the tooth forcing it's up up is causing the pain. There is way to relieve this pressure that works really well and stops the child from messing with it and lets you all get some sleep, and it is doctor mcleod's old scottish remedy. : take an egg cup and turn it up side down, there is a hollow under there. But the way let the child watch this performance. Open up your best bottle of scotch (of course single malt), and dispense the correct measure into the pitifully small dram container. Now, dip your pinkie into the medicine and then tasting of good scotch apply the tip of you finger over the site of the erupting tooth and press really hard. This will hurt and the child might well wince or even cry out, but the taste will distract them and they will know that you are doing it to help because that is what parents do and you will tell them so. Voila! the problem will be solved you will have accomplished two things. By pressing down hard you will stretch the thin membrane covering he tooth and by doing so as you take your finger away the cause of the discomfort is relieved. Secondly you will have established an appreciation for he taste of fine scotch early. You might want to sip up what is left in the egg cup. Don't be overly concerned, take you boy with you when you go to have your teeth cleaned next, and make sure that the receptionist knows that you want the doctor to take a look and make sure all is as it should be. Dr neil mcleod dds dentistry that lasts - quality that counts.
Wait. Even though your baby vomited it is impossible to know if any of the medicine stayed in their system or was absorbed. The safest thing to do as long as your baby is not having a high fever is to wait a few hours before giving him more tylenol (acetaminophen).