Teeth Whitening Techniques

I’m wondering if the reason why my gums bleed when I use the Colgate Visible-White system is caused by some nerve damage with my teeth or if it’s just me not being very capable of applying the right amount of gel. I only began using this gel recently, but I’ve had two sensitive lower teeth for quite a while after a surgery, so either of these issues is possible. Obviously I got a little too much gel on my gums, but it doesn’t seem to affect other areas as badly as these particularly finicky ones on the bottom. I’m not going to just deal with my gums bleeding and being sore for about an hour afterwards, just because that’s simply not healthy. And I probably won’t try any other kind of whitening system just because my dentist gave this one to me for free and I’m not vain enough to spend $60 on a new one. Any educated guesses as to what’s going on? Testimonials of similar issues?