As-salamu 'alaikum wa ra'hmatullahi wa barakatuhu wa maghfiratuhu. Sister, Jazak Allahu Khairan for being patient. Be satisfied with your what Allah has given you.
Allah Says in the Holy Quran Chapter 43 Surah Zukhruf verse 32: Is it they who would portion out the Mercy of thy Lord? It is We Who portion out between them their livelihood in the life of this world: and We raise some of them above others in ranks so that some may command work from others. But the Mercy of thy Lord is better than the (wealth) which they amass.
Allah Says in the Holy Quran Chapter 17 Surah Israa verses 18-21:
18 - If any do wish for the transitory things (of this life) We readily grant them-such things as We Will to such persons as We Will: in the end have We provided Hell for them: they will burn therein disgraced and rejected.
19 - Those who do wish for the (things of) the Hereafter and strive therefor with all due striving and have Faith, they are the ones whose striving is acceptable (to Allah).
20 - Of the bounties of thy Lord We bestow freely on all these, as well as those: the bounties of thy Lord are not closed (to anyone).
21 - See how We have bestowed more on some than on others, but verily the Hereafter is more in rank and gradation, and more in excellence.
So sister, don't be upset and depressed because of your condition.
Allah Says in the Holy Quran Chapter 2 Surah Baqarah verses 155-157:
155 - Be sure We shall test you with something of fear, and hunger, some loss in goods, or lives, or the fruits (of your toil), but give glad tidings to those who patiently persevere.
156 - Who say when afflicted with calamity: "To Allah we belong and to Him is our return."
157 - They are those on whom (descend) blessings from Allah and Mercy, and they are the ones that receive guidance.
Your parents are somewhat correct in their opinion, as muslim women now-a-days in this era of fitna-fasad, face many problems in work. However, Islam does allow muslim women to study, work or do business. But they must cover their awrah properly when they go outside.
Allah sub'hanu wa ta'ala says in the Holy Qur'an chapter 33 verse 59 -
"O Prophet, tell your wives and daughters and the believing women to draw their outer garments around them (when they go out or are among men). That is better in order that they may be known (to be Muslims) and not annoyed".
From this verse we know that the believing women are allowed to go outside after they dress themselves modestly.
It would be better if you be content with what Allah has bestowed upon you. But if you really want to earn money, be sure to acquire your parents permission first. Tell your parents to read this and then see what they say.
May Allah make your affairs easier. I am no scholar but I tried hard to answer your question. Forgive me for any mistakes. Jazak Allahu Khairan for reading this.