All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, sallallaahu 'alayhi wa sallam, is His slave and Messenger.
Firstly, we congratulate you for the blessing bestowed by Allah, The Exalted, upon you by giving you true understanding of Islam, guiding you to sincere repentance, and for your keenness on steadfastness in obeying Him. Evoking these beautiful and honorable meanings is one of the most important means to relieve your anxiety and depression; Allah, The Almighty, Says (what means): {Say, "In the bounty of Allah and in His mercy - in that let them rejoice; it is better than what they accumulate."} [Quran 10:58] So keep performing acts of obedience in order to savor reassurance of the heart. Ibn ‘Abbaas said: “Verily, a good deed gives brightness to the face, light to the heart, strength to the body, abundance in sustenance, and love in the hearts of the people.”
Secondly, you should remember Allah, The Almighty, frequently and keep your tongue busy with reciting Thikr; Allah, The Almighty, Says (what means): {Those who have believed and whose hearts are assured by the remembrance of Allah. Unquestionably, by the remembrance of Allah hearts are assured."} [Quran 13:28] Also, make sure to remind yourself with death, as it disciplines the self so it would not fall into greed or become afflicted by fear and dismay. The Prophet said: “Often remind yourselves with the destroyer of pleasures – death. Indeed, no one remembers death at a time of hardship, but he will feel ease, and no one remembers death at a time of ease, but he will feel constricted.” [Al-Bayhaqi in Ash-Shu‘ab, Ibn Hibbaan on the authority of Abu Hurayrah and Al-Bazzaar on the authority of Anas. Al-Albaani; Hasan]
Thirdly, do not allow this lack of resolve in worship to be a source of concern to you; it is normal. The Prophet said: “Oh, Hanthalah, an hour and an hour (i.e., there will be times when faith is weak and the worldly affairs will mix in one's heart with the Hereafter, while there will be times when faith is strong, and one's heart will be purely devoted to the Hereafter)” Rather, make such times a launching point to (recharge and) set off again. So continue seeking knowledge, attending gatherings of goodness, and keeping the company of righteous people.
Fourthly, do not let what you heard about some young Muslims, who were brought up with adherence to Islam and Sunnah and memorizing the Quran, discourage you from performing good deeds. Rather, make it a source of motivation for you to ascend to higher levels of perfection. The fact that they have preceded you (in performing good deeds) does not necessarily mean that they are better than you. If you diligently strive in doing good, you may surpass them (in rank). Therefore, you should perform a great deal of voluntary acts of worship after observing the obligatory ones, and be keen on performing the deeds whose benefit extends to others. At-Tabaraani narrated on the authority of Ibn ‘Umar that a man came to the Messenger of Allah and said: “O Messenger of Allah, who are the most beloved people to Allah and what are the dearest deeds to Allah?” The Messenger of Allah replied: “The most beloved among people to Allah is the one who is most beneficial to people, and the dearest of deeds to Allah are: to bring happiness to a fellow Muslim, or to relieve his distress, or to pay off his debt, or to satiate his hunger. To walk with my Muslim brother to fulfill a need for him is more beloved to me than to observe I‘tikaaf in this mosque (the Prophet’s mosque in Madeenah) for a month.”
Fifthly, yes, there are some texts related about the virtues of taking advantage of the time of youth in the obedience of Allah, The Exalted. For instance, Abu Hurayrah narrated that the Prophet said: “There are seven (types of people) whom Allah will shade in His (Throne's) Shade on the Day when there will be no shade except that of His (Throne's) … a youth who grew up in the worship of Allah.” [Al-Bukhaari and Muslim] Moreover, it was narrated in Musnad Ahmad on the authority of ‘Uqbah ibn ‘Aamir that the Prophet said: “Allah, The Exalted, (practices) 'Ajab (which entails that He is greatly pleased with) a youth who has no inclination (to worldly pleasures).” [Shu‘ayb Al-Arnaa’oot: Hasan] You are still young – praise be to Allah – so you will have a share of this merit, Allah willing. Verily, it is the bounty of Allah which He gives to whom He wills.
Allah knows best.