Is it possible to still feel pain or discomfort after your leg was amputated?

Yes. This is actually extremely common. It is called phantom pain. At least 2/3 of patients admit to phantom pain. Normal pain medications will not help. Some nerve medications may decrease symptoms. Also, touching the bottom of your stump will help to tell the nerves that the leg is no longer there. This typically improves over time.
Yes. The perception of pain or discomfort after amputation is called phantom pain. This can be felt at an absent limb or a portion of the limb. It has been known that at least 80% of amputees experience phantom sensations at some time of their lives.