There are a few first-hand accounts of the Third Crusade that have been translated into English.

Baldwin IV wasn't around for the Third Crusade, unfortunately - he died in 1185. Like most medieval kings, he didn't write very much. There are a few surviving charters though, which you can read here.

For works about Baldwin, the best place to look is Bernard Hamilton, The Leper King and His Heirs (Cambridge University Press, 2000)

For first-hand accounts of the crusade, there are:

Peter W. Edbury, trans., The Conquest of Jerusalem and the Third Crusade (Ashgate, 1998) - this is largely a translation of the Old French translation of William of Tyre's chronicle. William of Tyre was Baldwin IV's tutor and advisor and wrote a Latin chronicle of the Kingdom of Jerusalem, but he died in 1186, also before the Third Crusade. His chronicle was then continued by various other authors in French, and they write all about the crusade from the perspective of the local nobility.

D.S. Richards, trans., The Chronicle of Ibn al-Athir for the Crusading Period, Part 2 (Ashgate, 2007) - Richards translated 3 sections of Ibn al-Athir's chronicile, and part 2 covers the reign of Saladin and the Third Crusade. Ibn al-Athir isn't really an eyewitness source since he was writing in the 13th century, but he uses a lot of first-hand sources.

D.S. Richards, trans., The Rare and Excellent History of Saladin (Ashgate, 2002) - this is a translation of the biography of Saladin by Baha ad-Din, one of his advisors.

Franceso Gabrieli, Arab Historians of the Crusades, trans. E. J. Costello (University of California Press, 1969) - this one has translated excerpts from different time periods, but a lot of them are from the Third Crusade period and aren't available elsewhere (there are excerpts from Saladin's secretary Imad ad-Din al-Isfahani, which has otherwise never been translated into English, as far as I'm aware)

The Crusade of Frederick Barbarossa: The History of the Expedition of the Emperor Frederick and Related Texts, trans. Graham Loud (Ashgate, 2010) - Frederick died before reached the Holy Land but these texts were written by people who were travelling with him.

The Chronicle of the Third Crusade: The Itinerarium Peregrinorum et Gesta Regis Ricardi, trans. Helen J. Nicholson (Ashgate, 1997) - these texts are first-hand accounts from people travelling with Richard I of England

John T. Appleby, trans. The Chronicle of Richard of Devizes (Thomas Nelson & Sons, 1963) - Devizes also went on crusade with Richard. This one is a bit harder to find though!

O City of Byzantium: Annals of Niketas Choniates, trans. Harry J. Magoulias (Wayne State University Press, 1984) - Choniates is better-known for his account of the Fourth Crusade, but he was also present to give the Byzantine perspective on the Third.

Of course, it's also a good idea to read modern historical works about the crusade to better understand what's going on! Unfortunately there isn't really a recent history of Third Crusade, but here are some good starting points:

Jonathan Phillips, The Life and Legend of the Sultan Saladin (Yale University Press, 2019)

John D. Hosler, The Siege of Acre, 1189-1191 (Yale University Press, 2018)

Christopher Tyerman, England and the Crusades (University of Chicago Press, 1988)

John Gillingham, Richard I (Yale University Press, 1999)

John B. Freed, Frederick Barbarossa: The Prince and the Myth (Yale University Press, 2016)

Helen J. Nicholson, "Third Crusade", in The Crusades: An Encyclopedia, ed. Alan V. Murray (ABC-Clio, 2005)