Welcome to health care magic . Thank you for posting your query.
I can understand your concern.
At your height ideal weight is around 165-175 lbs. There is nothing wrong with you weighing 145 lbs. Yes , I can understand that you have a fast
metabolism.
First of all you must understand that to gain weight, you need to eat more calories than your body uses each day. You need to do this regularly. It's not enough just to have occasional extra snacks
Gradual weight gain is always advisable. An increase in 500 kcal per day can result in increasing the body weight by 0.5 kgs per week.
Eat plenty of healthy fats. Eat your egg yolks, meat with animal fat, coconut oil, and other healthy fats. Increase caloric intake - of the healthy kind ofcourse. So those bananas count well here.
Chew the food properly to improve digestion. This will help you even if you have a fast metabolism.
Keep a track of your weight gain as this is essential; it is healthy to increase approximately 5 to 6 kgs weight per month.
Try to do physical exercise for about 20 minutes a day.
Stick to this routine. Have patience.
The right combination of healthy food, exercise, right breathing, rest and sleep go a long way in a happier and healthier you.
Post any other question. We will be happy to help.
Have a nice day. Regards.