Check with your doctor to see if it is okay to give Tylenol to your 3 month old child, first.
Volunteer at a nearby day care center in their nursery to see how other babies that age act. That way you can see first hand how others your child's age interacts with their surroundings.
Listen to your "mother". There are lots of senior mothers out there who have raised their own children, grandchildren, or neighbor's children.
Visit other mothers your age with children. This web site is a good place to start. Keep up the good work.
Pray!!! God bless you and give you wisdom in how to raise the gift that He has allowed you to bring into this world for some reason. Ask Him to direct you daily and He will show you how to train up this child in the way she/he should go.