Firstly: 

The martyrs of this ummah are many, praise be to Allah. The one who is killed or dies (in jihad) for the sake of Allah is a martyr; the one who dies defending his wealth or property is a martyr; the one who dies defending his honour is a martyr; the one who dies of the plague is a martyr; the one who dies by drowning is a martyr; the one who dies of pleurisy is a martyr; the one who dies of a stomach ailment is a martyr; the one who dies by burning is a martyr; the one who dies under a collapsed wall or building is a martyr; and the woman who dies in childbirth is a martyr. 

See the answer to questions no. 4017, 93105 and 151904 

Secondly: 

There is no shar‘i evidence – as far as we know – to suggest that the one who suffers difficulty in breathing then dies as a result of suffocation is regarded as a martyr, but at-Tabaraani narrated in al-Mu‘jam al-Kabeer (6115) from Salmaan that the Prophet (blessings and peace of Allah be upon him) said: “Being killed for the sake of Allah is martyrdom; dying of the plague is martyrdom; dying in childbirth is martyrdom; being burned to death is martyrdom; drowning is martyrdom; tuberculosis is martyrdom and dying of a stomach complaint is martyrdom.” 

Classed as saheeh by al-Albaani in Saheeh al-Jaami‘, 3691 

Tuberculosis is a disease that affects the lungs in which the person becomes emaciated and dies. 

Al-Mu‘jam al-Waseet, 1/445 

However, there is no clear indication that the one who dies as a result of difficulty in breathing is a martyr. The status of martyrdom is a special status before Allah, and not everyone who dies of sickness attains it, even if he is one of the righteous close friends of Allah. Rather it is a status concerning which we adhere to what is mentioned in the texts, and we do not know of any shar‘i text that suggests that the one who dies as a result of difficulty breathing is regarded as being one of the martyrs. But there are many other positions of virtue and reward before Allah apart from that, and Allah’s bounty towards His slaves is abundant. 

Thirdly: 

We do not know of any shar‘i evidence to suggest that having a nosebleed as death is approaching is one of the signs of a good end. 

The signs of a good end were mentioned by Shaykh al-Albaani (may Allah have mercy on him) in Ahkaam al-Janaa’iz (pp. 34-46). We have mentioned them in the answer to question no. 10903, and this is not one of them. 

And Allah knows best.