It's possible that the burning sensation you're experiencing when urinating could be due to irritation of your urethra. Masturbation itself does not usually cause damage to the urethra, but vigorous or rough handling may lead to temporary irritation.
Since you mentioned no other symptoms like frequent urination or discharge and seem otherwise comfortable, it might just be a minor issue. However, if the burning persists or worsens, it would be best to see a healthcare provider for further evaluation and appropriate treatment.
Remember always prioritizing your comfort and health is essential!