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.
First of all, you should know that marriage, like other livelihood, is predestined, and a Muslim gets what is predestined for him, and the whole matter is in the hands of Allaah. Allaah says (what means): {And there is no creature on earth but that upon Allaah is its provision, and He knows its place of dwelling and place of storage. All is in a clear register.} [Quran 11:6]
Al-Bayhaqi and Al-Baghawi quoted in Sharh as-Sunnah that Ibn Mas’ood narrated that the Prophet said, “Jibreel (Gabriel) inspired in my heart that no soul will die until it would have consumed its (designated) provision, so seek your provision in moderation.”
The delay of marriage does not necessarily mean that it is a punishment for a sin. It can be a mere test; so we advise you not to worry about this matter and to be patient. The good of this world and the Hereafter lies in patience. For texts on the reward of patience, please refer to fatwa 83577.
You should supplicate Allaah as much as possible as this is the best means to achieve one’s needs, and Allaah is Most Kind and Most Generous, and He answers the supplication of those who supplicate Him, and He never disappoints those who have hope in Him. Allaah says (what means): {And your Lord says, "Call upon Me; I will respond to you." Indeed, those who disdain My worship will enter Hell [rendered] contemptible.} [Quran 40:60]
Salmaan narrated that the Prophet said, “Your Lord is bashful to turn away His slave empty-handed (i.e. not responded to) when he raises them (his hands) to Him asking Him for any good.” [Abu Daawood, At-Tirmithi and Ibn Maajah]
Indeed, your parents did well by searching for a husband for you; this is indeed a way that the righteous people followed. ‘Umar proposed his daughter Hafsah to Abu Bakr and ‘Uthman but they both refused as they knew that the Prophet wished to marry her.
You as well can search for a suitable husband provided the Islamic etiquette is observed. Verily, a woman proposed herself to the Prophet for marriage, and the Prophet did not object to her act. For more benefit, please refer to fatwa 82471.
Besides, you did the right thing by stopping that relationship with that young man as it is not permitted for a man and a non-mahram (marriageable) woman to have an affectionate relationship. However, just stopping that relationship is not enough, you are also required to sincerely repent. For benefit on the conditions of repentance, please refer to fatwa 86527.
Furthermore, we do not think that you were wrong when you took the feelings of your parents into account and refused that young man's offer to propose to you. However, if he repented and still wants to marry you, then try to persuade your parents to accept him to marry you. The age difference does not Islamically prevent from marriage, and the difference of age between you and him is insignificant.
On the other hand, if marriage will be delayed for a long time after engagement, then we do not advise you to accept his proposal. The engagement period being too long may lead to impediments that may prevent the completion of the marriage after a long wait. So try to perform the istikhaarah prayer before taking any step; and please refer to fatwa 81434. The istikhaarah prayer means putting the matter in the Hands of Allaah to choose the best for you; after that, you will feel relaxed and reassured regardless of whether the marriage is concluded or not.
Allaah knows best.