Sara, I am on a ton of heparin, too. Try not to worry, I doubt your doctor will put you on too high a dose.
It is a bit strange that you are on it three times a day, though. Heparin has a half life of 12 hours so if you have it twice a day you are more than covered. Most ladies only have it once a day.
What brand are you on and what dose if you don't mind me asking?
Did they do an anti-Xa (X reading as 10) blood test and that is what triggered your new dose? If yes (and this is probably asking way too much detail), do you have a target range?
Sorry about the 20 questions. I've spent the past three years on and off heparin so I'm quite interested in the subject. How sad am I?!