Parents not allowing me to fast in Ramadhan

To be fair from the outset, I must declare that I am an atheist and therefore Haram in the eyes of Islam.
I promise that I have done my best to research in a way that is honors your faith absolutely.
If you have any doubts, this is your opportunity to turn away.

Interested in your question and in [i]answering it in accord with Islam[/i],
I did a bit of research across several sites and came across the following, which is what I would call a fundamentalist Sunni approach.

(Personally, I don't believe it is necessary to be quite that extreme, especially is it makes life difficult for you in your family, community and the wider culture of wherever you live.)
According to the Qur'an, Allah rewards the pure in heart - and that is what is most important.
He is also merciful to those who sincerely repent and reform their ways.
But it is goodness, love, charity, honesty and integrity that he rewards most. He sees the truth in the depths of each mind and heart.

From ([u]https://myislam.org/reasons-for-not-fasting-during-ramadan/[/u])
First, as you probably already know, a Muslim woman is required to have her own direct relationship with Allah, and act in accordance with her own understanding of the Qur'an and the Hadith.
The halal exemplars among women are agreed to be:
Khadija bint al-Khuwaylid, the Prophet's first wife;
Fatima bint Mohammed, the Prophet's daughter from Khadija;
Zainab, Fatima's daughter by her husband, Ali;
Aisha bint Abu Bakr, the Prophet's 12th, last and youngest wife - learned in reading and writing classical Arabic, had memorised the Qur'an, and accredited with narrating over 2,000 hadith, or the sayings and doings of the Prophet Muhammad.
There are others who were famous for their devotion, but these four were widely known for their learning, exceptional intelligence, wisdom. And their advice which Mohammed requested, respected and supported.
This shows that even from the earliest times, a Muslim woman's faith and relationship with Allah and his will were highly valued.

Ultimately, you need to make a decision in accord with your own conscience, and be prepared to explain it to your parents.

The Qur'an states that the following exemptions apply: [i]the insane; children who are not adolescent yet; the elderly and chronically ill for whom fasting is unreasonably strenuous[/u]; Such persons are required to feed at least one poor person every day in Ramadan for which he or she has missed fasting.[/i]
From the Surah Al-Baqarah Ayah 183

“…[i]whoever is ill or on a journey – then an equal number of other days. Allah intends for you ease and does not intend for you hardship and [wants] for you to complete the period and to glorify Allah for that [to] which He has guided you; and perhaps you will be grateful[/i].” Surah Baqarah Ayah 185

The same article also quotes the Hatdith on special circumstances in which it is incorrect or unnecessary to fast, or proper to say half the prayers and make specific numbers of compensations (acts of charity) later. In particular, it says that Allah wishes the fasting to be [i]never[/i] a cause of suffering or ill health.
references:
Sahih al-Bukhari 50,
Ibn Qudaamah in al-Mughni (4/403)
Hasan (Darussalam) Ibn Majah English reference: Vol. 1, Book 7, Hadith 1667,
and
Muwatta Malik Book 18, Hadith 49

So...
Ask your Mum to take you to see your family doctor.
If he or she says you are dangerously underweight,
[i]please be guided by his/her professional advice[/i].
Under those circumstances,
[i]you would definitely not be sinning against Allah's commandments[/i].

May peace be with you.

P.S. I believe all people have the right to follow their own faith exactly as they see fit.
I believe it is wrong and harmful to try to interfere with other's beliefs or convert them to my own views.
Though I would intervene if it meant someone was likely to harm themselves, another, an animal, or the ecological health of Earth and its atmosphere.

Wa alaykumu s-salam

Wa Alaykum Assalaam wa Rahmatullah

Parents are humans. Just know that your parents are not an excuse to turn away from an obligation if you wish to be following the path of Allah.
In Islam, we submit to Allah and His commands. We're free to listen to Allah or turn away.
My parents told me so is not an excuse.

However, there are conditions. You are not obligated to fast under extreme conditions or if you're sick.
https://quran.com/2/184
So take care Allah first, then yourself, then your parents. Always be kind, polite, and show them mercy. You're allowed to ignore any poor commands from your parents. (I am sure that where you are, respect for your parents is of high importance)

Just know that Haram and Halal are prescribed by Allah in Islam. Your parents don't come before their Creator if they're Muslims and saying they wish to follow Allah.

Also, search for what Islam has on this by trusted scholars as well. Lots of things can be found on YouTube videos from trusted scholars.

Ramadan Kareem
I think obeying your parents trumps fasting Ramadan.

You will never be saved by religious observance. You are saved by Faith not by works.

you're an adult. Maybe time to grow up and not let others dictate when you eat or not 🤷‍♂️

I don't know about Islam, but other religions have dispensations on these things when your health is threatened