Funny, but I went through the same thing when I first started ... which was only a few months ago.
The best advice I can give in this situation is to become comfortable with handling the blade first.
For me, this was the difference between scraping and shaving.
Pre-Shave Prep is a really big deal, believe it or not. I find myself prepping and re-prepping areas because it still takes me some time (30 minutes or so) to get through a full 2-3 pass shave.
I have sensitive skin as well and I have found that a pre shave oil without lather does the trick. I cant see what the blade is doing when it is covered up with shave soap. Never really did like shaving creams or soaps to begin with. Olive oil is my friend. Also I have found that hair conditioner works really well. I usually use some conditioner on the beard area in the shower. Post shower comes the hot water/hot towel then the oil.
Hey, it works for me.:shrug:
As far as me chin .. well ... that area for me is a tough one as well. I never realized how tough the hair on me chin and moustache area really is.
I have found that when my blade handling technique suffers, I get scraped up skin. Usually this is from me pushing the blade into the skin to cut the hair. At first, I was impatient and would push through the chin area. The result? Not slicing off too much hair and getting really scraped up in the process.
A gentle touch, good prep, and lots of skin streching usually gives me a decent shave regarding the chin area. Like I said before ... I am still learning.
For me, I would rather leave some hair and not get all tore up than to try and get a great shave and get torn up ... and still have remaining hairs. Grrr.
Hope this helps.