Need visa for brother to travel with me to UK

In commentary you explained "women preferably don't travel alone" and therefore you need your brother to accompany you so that you can sit an exam.

I expect that you will have difficulty establishing a premise for your brother to accompany you to the UK for the purposes of providing family supervision. The point being that people who have attained a physician's qualification will visit the UK and sit their examination as an independent adult.

Granted that customs and traditions influence the way that people explain their rationale for visiting the UK, the decision-makers are not obliged to treat this type of premise as substantial; this is especially true if the applicant(s) would not qualify in their own right. You pointed out that your brother requires 3rd party sponsorship, and what this amalgamates to is that he has neither premise nor means to qualify independently.

What makes it worse is that you have already applied for your entry clearance and were in a position at that time to know that your family would place constraints on your travel. But based upon your narrative, he did not apply along with you. This would raise a big-time question mark for the decision-maker and it would be very difficult to see it resolved in your favour.

What about my mum and younger brother?

The same reasoning applies here. If you require family supervision in order to travel, you would have known about it earlier and explained it when you made your application. When they see applications arrive from your family members on a premise that you cannot travel alone, they would be entitled to suspect (if not conclude outright) that you had not disclosed your circumstances in a transparent manner.