My 3 yr old has a fever of 101.9 I gave her tylenol (acetaminophen) five minutes before she throw it all up. Do I give her more tylenol (acetaminophen)?

YES. My general rule on meds is a barf within 15 minutes can be followed by a full repeat of the dose. It may be prudent to wait until the kid has held down some sips of water or other material before trying.
Tylenol (acetaminophen) vomited out. Agree you need to rpeat the dose if the child vomited it right away. You may want to try giving it as a rectal suppository.
Evaluate symptoms. Fever is part of the body’s natural defense mechanism, so fever not only signals illness; a fever can help your child's body fight off infection. If your child is uncomfortable from the fever, it is ok to give the appropriate dose of Acetaminophen orally, and the medication also comes in a rectal preparation. Ibuprofen is also an alternative.