Fuck the Middle Ages, let's take it back to 1213 BC. Check out this grandpa:
Maybe you don't recognize it? Maybe this will help you:
Don't you recognize him yet?
This is Pharaoh Ramesses II, also known by his Greek name Ozymandias, of the 19th Dynasty; the most powerful and longest-reigning pharaoh of ancient Egypt. In fact, not only was he Egypt's longest-reigning pharaoh (edit; the second-longest reign after Pepi II), he is actually one of the longest-reigning monarchs in human history, having reigned for 66 years and 2 months. He was approximately 91 years old when he died, having outlived most of his wives and even most of his children. At the time of his death, however, Ramesses II had severe arthritis and hardening of the veins. He likely walked hunchbacked for the last ten years or so of his life. He also had severe tooth decay, and it is speculated that a dental infection may have actually caused his death.
So, to answer your question, yes, it was possible in the Middle Ages, and even long before the Middle Ages, for people to live to 90 or even 100 years old, but it was rare. In fact, most children didn't reach adulthood even 100 years ago. Medical treatments until 1500 consisted essentially of herbal concoctions, prayers, and rituals. Even something as trivial as a fresh wound or a small graze on the flesh could have been a death sentence, and the older you got, the more vulnerable you became.