Am I entitled to claim the profits generated from my brother's investment of my money, which I deposited with him twenty years ago, or should I only demand the original amount?

If the money given was a deposit, then it must be returned upon request, and he is not permitted to dispose of it without your permission. Otherwise, he would be transgressing and would be liable for any decrease in the money, and there is a difference of opinion regarding his entitlement to profit.

However, if the money was a loan, then it must be returned upon request, unless the debtor is in straitened circumstances, due to the Almighty's saying: "And if there is one in [financial] difficulty, then [let there be] postponement until [a time of] ease," and due to the Prophet's (peace be upon him) saying: "Delay by a rich person is oppression," and "The procrastination of one who can afford it makes his honor and punishment permissible." The lender is not entitled to any profits.