Not only the prophet Muhammad (peace and blessings be upon him) is infallible, all Prophets and Messengers of Allah are infallible. They are the chosen persons for the very aim of guiding people to their Lord. In this sense, they offer the best example of perfection and beauty. One review on the biography of the Prophet (peace and blessings be upon him) will show how great and perfect he was. If we are to talk about the aspects of his greatness, ages and ages will not avail us to do that. For elaboration on some of the aspects of this great personality, you can read:

Dr. Ja`far Sheikh Idrees, professor of Islamic studies, Institute of Islamic and Arabic Sciences, Washington, states that: “Messengers are human beings chosen by Allah Who gave them the honor of conveying His message to other people. Being such a Messenger is not a position that one attains by any consciously designed effort. It is a grace from Allah, who grants this grace to those who deserve it. Messengers are not then, like the rank and file of us. True, they are men but they are men of an extremely high moral, spiritual and intellectual standard that qualifies them, in Allah’s Sight, to be the bearers of His light to the world. Asked about Prophet Muhammad’s conduct, his wife `Aishah said, “It (his conduct) mirrored and typified the (teachings of) Qur’an,” meaning that he embodied all the ideals which the Qur’an presents.
two related points about Messengers, as the Qur’an stresses, and which therefore deserve some elaboration, are the humanity of Prophets and the nature of their task.
Despite the vast spiritual, moral and intellectual difference between them and ordinary men, and despite their closeness to Allah Prophets were nonetheless humans with all that this term implies. They begot and were begotten; they used to lead a normal life, eating, drinking and going about in market plates. Almighty Allah says: “We never sent before thee any Messengers but lo! they ate food and walked in the markets. And We have appointed some of you a test for others: Will ye be steadfast? And thy Lord is ever Seer.” (Al-Furqan: 20)
So part of their nature was governed by the nature of human beings; they used to
sleep and when their time came they died; they used to forget and err. Allah says: “And Adam disobeyed his Lord, so went astray. Then his Lord chose him, and relented toward him, and guided him.” (Taha: 121-122)
Their knowledge was limited; and could therefore tell only that part of the future which Allah revealed to them. They cannot intercede with Allah on behalf of any person except with His permission, and it was not left to them to cause people to go in the right path. In short, they had no part to play in the running of the affairs of the universe. Many early Muslim scholars have observed that to emphasize the humanity of the Prophet the Qur’an called him ‘servant of Allah’ on the three occasions on which he was honored.
Messengers were entrusted, as we’ve said above, with the task of conveying Allah’s word to other people. But this is not as simple as it looks. It implies many things which are not at first sight clear, and which the Qur’an therefore expounds and elaborates.”
In addition, we would like also to cite for you what is written in the Kuwaiti Encyclopedia of Jurisprudence; it reads:
“Infallibility means Allah’s protection of man from involvement in sin a way that it will be impossible for him to commit it. This applies to angels and Prophets. Concerning angels, Almighty Allah says: “…who resist not Allah in that which He commandeth them, but do that which they are commanded.” (At-Tahrim: 6)
as regards Prophets, they are infallible in the sense that they are given immunity to getting involved in apparent sins such as telling lies and internal sins such as envy, conceitedness and showing off. Being the best example to be followed, it’s natural for every Prophet to be free from sin in word and deed. Allah commanded all people to follow their own P
rophets and Messengers. In this regard, Almighty Allah says: “Verily in the Messenger of Allah ye have a good example for him who looketh unto Allah and the last Day, and remembereth Allah much.” (Al-Ahzab: 21)
By and large, we are to say that after receiving the honor of prophethood, all Prophets and Messengers are protected from involvement in sin.
now what about their state before receiving the honor of being Allah’s inspired Messengers? This issue is controversial. While a group of people say that Prophets were also infallible in that period, others hold the view that they were fallible. The correct view, however, is that the Prophets enjoyed all-time infallibility; before or after receiving Divine mission. Before receiving Divine revelations, their status can be clarified in either of the two ways; there might not have been any Divine law that would forbid or command certain acts, thereby there would be no need of infallibility. But the inner pure nature of a Prophet requires his being a great and excellent example and his being far from involvement in any error.
the second possibility is that a Prophet might have been an adherent of a former divine legislation sent with another previous Prophet, as is the case with Prophet Lut who was the follower of Prophet Abraham. But in this case also there is no decisive evidence of their infallibility in that period.
however, the biography of all prophets and Messengers draws portraits of clarity, purity and noble manners and makes it crystal clear that they were as far from sin as the west is far from the east.”