shoot has 29 distinct synonyms spread across 11 of its 22 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
send forth suddenly, intensely, swiftly
“shoot a glance”
emit (as light, flame, or fumes) suddenly and forcefully
“The dragon shot fumes and flames out of its mouth”
cause a sharp and sudden pain in
“The pain shot up her leg”
variegate by interweaving weft threads of different colors
“shoot cloth”
utter fast and forcefully
“She shot back an answer”
measure the altitude of by using a sextant
“shoot a star”
give an injection to
“We injected the glucose into the patient's vein”
Synonyms, antonyms and the broader and narrower relations for shoot come from Princeton University’s WordNet. Full sources and licences.