Yes you would need to make a stock and dilute in this case. That's generally good practice because even with a very sensitive scale it can be difficult to weigh such tiny amounts.

Do you mean you need 0.2 mg gentamicin total in 10 mL of solution (0.02 mg/mL concentration), or do you need it at 0.2 mg/mL concentration (2 mg in 10 mL)?

I need 0.2 mg gentamicin total in 10 ml of solution. Alexandra Johnson