Are there thumb guitar pics that pick from the side of your thumb- like I do when I pic without it?

Standard thumb picks do stick out to the side of the thumb. They are available at most music stores. They are made of plastic and can be trimmed to suit your particular playing style. Keep in mind that most finger picking done on guitar does not use picks, just the fingers. Guitarist often will keep their nails trimmed to a specific length to help develop a nice callous on their picking fingers. This is usually known as "fingerstyle" guitar. There are plenty of books and videos available on the subject.