When the mind is full of doubts or depressed, how do I convince myself that the fears that come up are not true?
When the mind is full of doubts or is depressed, it means that the level of prana has come down. When the level of prana goes down, doubts arise and we become sad. So, the remedy is to increase the prana level, through pranayama, proper food, exercise, singing and fasting.
Go on a fruit diet for a few days. We keep on stuffing ourselves with food, even if we are not hungry.