SHOCKING CUSTOMER SERVICE

I booked a BA flight to Cape town 6 months ago for myself and my wife. We arrived 1.5 hrs early to check in on 8 Dec 2017, 6.20am flight BA 6300. Ar check in we were told that we cant fly as the flight is full?! They said we can fly on the later flight and thst we DEFINITELY cannot get onto our flight because sales had over booked the flight!! We had to be in CT at 9am... SHOCKING BA!!! In the last minute they told us we could get on IF WE RAN TO GATE 17. We had to take our suitcase into the plane. We ended up on the flight..SWEATY and stressed!!!