The term shrimp is used to refer to some decapod crustaceans, although the exact animals covered can vary. Used broadly, it may cover any of the groups with elongated bodies and a primarily swimming mode of locomotion – most commonly Caridea and Dendrobranchiata. In some fields, however, the term is used more narrowly and may be restricted to Caridea, to smaller species of either group or to only the marine species.
Yes, eating shrimps is allowed in Islam. In fact, out of all water animals, only scaled fishes and shrimps are allowed to eat. All unscaled fishes and other water animals e.g. crabs, lobsters, oysters, shells, etc are Haraam to eat.
Thank you for your question. Shrimp is allowed according to the rulings of Sayyid Sistani. Please refer to the below Q&A from his website:
Question: What kind of marine animals are halal?
Answer: It is not permissible to eat from marine animals anything except fish that has scale; shrimp is considered from that category [of permissible sea animals]. But other than fish, like lobster, and similarly the fish that does not have scale is forbidden. Allãh knows the best.
May you always be successful.
As far as sea food is concerned, only that fish which has scales may be consumed. In addition, it must be alive when caught from the water. Crabs are not classified as fish and may not be consumed. There is some differences amongst certain ulama' regarding lobsters but the general consensus seems to be that it should not be consumed. See Ayatullah Seestani's Islamic Laws p. 489.