I am 20 years old 5ft tall small frame and weigh 90 lbs. I eat well but can't manage to get over 95 lbs! Is this normal?

Gaining can be tough. At 5 feet and 90 pounds, your bmi (body mass index) is 17.6. (google up bmi calculator) underweight is defined as a bmi less than 18.5. To gain one pound, you must eat 3500 calories more than you use. It may be easier to break this down to 500 calories per day to gain a pound per week, or 250 calories per day to gain a pound every two weeks. Make sure the extra food is healthy: greek yogurt, etc.
Yes. It sounds like its normal for you.What about your parents?Are either of them of similar frame?