Your doctor is right in avoiding 'sleeping pills' at your age as they can have serious side effects like confusion and falls.
Here are a few things that will help your sleep.
First, avoid sleeping in day time. If you must, sleep only for about half an hour. Avoid lying in bed during day more than an hour.
Keep the same waking time each day.
Take mild exercise and stay active.
Avoid bright light and noisy room for sleep.
Don't take tea/coffee in evening/night.
Develop a relaxing routine before sleep time.
People in old age tend to sleep earlier and get up earlier. Therefore, if you are sleepy early at night, don't postpone sleep.
If other than sleep, you have other problems such as persistent sad mood, increased irritability,
tiredness, loss of interest, feeling that life is not worth living any more, you should
consult a psychiatrist.
Hope this answers your question.