I am a woman who always thinks about death and fears that it might come suddenly and feel that I am negligent in performing acts of worship and obedience to Allaah The Almighty.
I also feel much pain when I see those around me committing sins and being heedless of the wrath and punishment of Allaah The Exalted.
Please advise me, may Allaah reward you.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

There is no doubt that remembering death and fearing it is required under the Sharee‘ah, as the Prophet, sallallaahu ‘alayhi wa sallam, said: “Remember often the destroyer of pleasures  (i.e. death).” [An-Nasaa’i, At-Tirmithi, Ibn Maajah and Ahmad, Al-Albaani: Saheeh (Authentic)]

Imaam Al-Qurtubi said,

Ad-Daqqaaq said that whoever remembers death frequently will be blessed with three things: swiftness in repentance, satisfaction of the heart, and activeness in performing acts of worship. On the other hand, anyone who forgets death will be punished by three things: procrastination in repentance, discontentment, and laziness in performing acts of worship. [At-Tathkirah, Part One, p. 27]

As-Suddi interpreted the Quranic verse in which Allaah The Almighty Says (what means): {[He] Who created death and life to test you [as to] which of you is best in deed,} [Quran 67:2] saying, “That is, to test you as to which of you is more frequent in remembering death, best in preparing himself for it, and best in being prepared for it and fearing it.”

Hence, every Muslim is required to remember death, endeavor in doing good deeds, avoid procrastination in repentance and combine between hope in reward and fear of punishment; Allaah The Almighty Says (what means): {Is one who is devoutly obedient during periods of the night, prostrating and standing [in prayer], fearing the Hereafter and hoping for the mercy of his Lord...} [Quran 39:9]

In other words, fear of death should never lead to despair or loss of hope in the mercy of Allaah The Almighty.

Similarly, hope in the mercy of Allaah The Almighty should not lead to laziness or negligence in acts of worship, not to mention the committing of sins.

Likewise, feeling pain when seeing sins and disobedience to Allaah The Almighty is praiseworthy and is a form of forbidding evil; moreover, a Muslim should forbid anyone who commits a sin and advise and guide him wisely and leniently.

It is enough in this regard to mention the Hadeeth in which the Prophet, sallallaahu ‘alayhi wa sallam, said: “Whoever calls to righteous acts will attain the same reward as those who follow him without their reward being diminished in any respect.” [Muslim]

Hence, we re-assure the honorable questioner and ask her not to worry about how she feels, because she is in a good condition, if Allaah wills.

May Allaah increase your keenness on performing good deeds. We also advise you to read the Quran frequently as well as ask Allaah to exalt the mention of the Prophet, sallallaahu ‘alayhi wa sallam, as much as you can, since remembrance of Allaah The Almighty pacifies the soul and protects one against the devil and his whispers. Allaah The Almighty Says (what means): {Those who have believed and whose hearts are assured by the remembrance of Allaah. Unquestionably, by the remembrance of Allaah hearts are assured.} [Quran 13:28]

You should also be keen on accompanying righteous women and performing prayers at their due time as well as acquiring knowledge.

May Allaah The Almighty guide you to what He loves and to what pleases Him.

Allaah Knows best.