Yes. Absolutely teeth can be made longer. If you pay attention to bite and speech issues that may arise and design the teeth properly then longer teeth that fit the proportions of your face better can definitely be achieved. Options can include veneering the teeth with either composite bonding or porcelain. Sometimes the teeth are covered by too much gum tissue and can be made longer in appearance simply by removing some of the excess tissue.
Yes, cosmetic dentists can make teeth longer and even change their shape with porcelain veneers. This is most effective on the upper front six or eight teeth, and does not work that well on bottom front teeth. To make all the teeth longer would involve full mouth reconstruction, which is quite involved and costly. However, the porcelain veneer treatment may be all that you need to give you a more "adult-like" smile.
Please feel comforted in knowing that your displeasure on having small teeth and wanting to do something about it is not at all uncommon. Fortunately, with today's modern cosmetic dentistry techniques those issues can be very successfully treated.
Teeth can definitely be made longer. There are many options available to you depending on the specific condition of you mouth and why you teeth are short. I would suggest you find a dentist who is well educated in these options and have an evaluation done. The two of you can come up with a plan to achieve your goals. Good luck!