Insha’Allah you are well. Some recommendations:

1- When you approach your mother, show her that your decision is not emotional but rather intellectual. Tell her that you have been thinking about how Islam recommends marriage. How marriage completes religion. How marriage is an opportunity to raise good children. Tell her you want to follow the Sunnah of the Prophet (s) because he knows what’s best for us. Be creative and effective in using these points. They could convince her Insha’Allah. Also, show her that you will stay committed to your education and that you have a plan to manage your education and marital life. This is important to your parents.

2- Have someone else talk to your mother on your behalf—like a friend, a sibling or a family member. Sometimes if someone else advocates for you it can be more effective.

3- Another alternative is to get to know the brother a little more to make sure he has a good character. Once you have verified that, just tell him to come and officially propose. I know this will sound awkward to you, but sometimes it does actually work. When parents see the man coming officially to them to propose, and he is not having a relationship with their daughter behind their back, they will know he is serious and not fooling around. There is a good chance they’ll accept. They might not want to rush it, but they’ll give you the opportunity.

May Allah facilitate it for you.