The Piccadilly and the District lines don't run from Waterloo. Therefore, as I said above, you need to get the Jubilee line to Westminster, then change onto the District line to Hammersmith. Journey time for that is probably about 20 minutes, according to the route planner. You then need to either walk or get a bus down Fulham Palace Road to the clinic; it's about 10 minute walk.
It's a really easy journey, don't worry about it too much. Just make sure you leave yourself plenty of time to get there so you're not late for your appointment.