The book of Psalms contained prophecies about Christ. So, I think Christians called David a prophet too. Im sure you already knew that (about the Psalms) as a Christian, so what do mean by this?: “As far as I know David is not considered a Prophet by anyone other than Muslims…”.
An error on my part regarding David. Islam (Qur’an) lists about 25 individuals as prophets but acknowledge more that go unnamed, where the Jews list about 55 major and minor prophets. I will accept the Jews listing, which does include David but not others.
Islam:
Adam
Idris (Enoch)
Nuh (Noah)
**Hud
Saleh **
Ibrahim (Abraham)
**Isma’il (Ishmael) **
Ishaq (Isaac)
Lut (Lot)
Ya’qub (Jacob)
**Yousef (Joseph) **
**Shu’aib **
**Ayyub (Job) **
Musa (Moses)
Harun (Aaron)
Dhu’l-kifl (Ezekiel)
Dawud (David)
Sulaiman (Solomon)
Ilias (Elias)
Al-Yasa (Elisha)
Yunus (Jonah)
Zakariyya (Zechariah)
**Yahya (John) **
**'Isa (Jesus)
Muhammad **
The bolded names are not recognized as prophets by Jews or Christians.
Jews:
The following list of prophets is based on the Talmud and Rashi.
Abraham Gen 11:26 - 25:10
Isaac Gen 21:1 - 35:29
Jacob Gen 25:21 - 49:33
Moses Ex. 2:1 - Deut. 34:5
Aaron Ex. 4:14 - Num. 33:39
Joshua Ex. 17:9 - 14, 24:13, 32:17 - 18, 33:11; Num. 11:28 - 29, 13:4 - 14:38; 27:18 - 27:23, Deut. 1:38, 3:28, 31:3, 31:7 -Joshua 24:29
Pinchas Ex. 6:25; Num. 25:7-25:11; Num. 31:6; Josh. 22:13 - Josh. 24:33; Judges 20:28
Elkanah I Samuel 1:1 - 2:20
Eli I Samuel 1:9 - 4:18
Samuel I Samuel 1:1 - I Samuel 25:1
Gad I Sam 22:5; II Sam 24:11-19; I Chron 21:9-21:19, 29:29
Nathan II Sam 7:2 - 17; 12:1 - 25.
David I Sam 16:1 - I Kings 2:11
Solomon II Sam 12:24; 1 Kings 1:10 - 11:43
Iddo II Chron 9:29, 12:15, 13:22
Michaiah son of Imlah I Kings 22:8-28; II Chron 18:7-27
Obadiah I Kings 18; Obadiah
Ahiyah the Shilonite I Kings 11:29-30; 12:15; 14:2-18; 15:29
Jehu son of Hanani I Kings 16:1 - 7; II Chron 19:2; 20:34
Azariah son of Oded II Chron 15
Jahaziel the Levite II Chron 20:14
Eliezer son of Dodavahu II Chron 20:37
Hosea Hosea
Amos Amos
Micah the Morashtite Micah
Amoz (the father of Isaiah)
Elijah I Kings 17:1 - 21:29; II Kings 1:10-2:15, 9:36-37, 10:10, 10:17
Elisha I Kings 19:16-19; II Kings 2:1-13:21
Jonah ben Amittai Jonah
Isaiah Isaiah
Joel Joel
Nahum Nahum
Habakkuk Habakkuk
Zephaniah Zephaniah
Uriah Jeremiah 26:20-23
Jeremiah Jeremiah
Ezekiel Ezekiel
Shemaiah I Kings 12:22-24; II Chron 11:2-4, 12:5-15
Barukh Jeremiah 32, 36, 43, 45
Neriah (father of Barukh)
Seraiah Jeremiah 51:61-64
Mehseiah (father of Neriah)
Haggai Haggai
Zechariah Zechariah
Malachi Malachi
Mordecai Bilshan Esther
Oded (father of Azariah)
Hanani (father of Jehu)
Female Prophets
Sarah Gen 11:29 - 23:20
Miriam Ex. 15:20-21; Num. 12:1-12:15, 20:1
Deborah Judges 4:1 - 5:31
Hannah I Sam 1:1 - 2:21
Abigail I Sam 25:1 - 25:42
Huldah II Kings 22:14-20
Esther Esther