I have lots of blackheads around my nose, and your best bet is to use concealer and foundation with medium coverage, because full coverage might look a little cakey (blackheads are usually in groups in a certain area, and I've found that using a full coverage concealer just cakes up in the areas between the bumps.)
For medium coverage, you want to get a concealer that comes in a tube, as pot concealers are usually full coverage and wand concealers tend to be too liquid-y. I recommend the Clinique Advanced Concealer. (pictured)(I believe that most Clinique products are fine for sensitive skin). It also contains medications that help to treat acne.
Another one I recommend, though it may be too thick (which can lead to caked up concealer), is the Murad Acne Treatment Concealer. It is also good for sensitive skin and does well with treating blackheads. You just have to be careful not to apply too much, and to blend well.
Overall, most Clinique products are just fine for sensitive skin (that's one of the things they're known for!). So I would recommend the Clinique Even Better Makeup SPF 15 as a foundation. Put a few dots where you have problems (before or after concealer, it's a personal preferance. But if your concealer doesn't quite match your skin tone, I'd do that first. If not, I'd recommend using foundation first, because then you use less concealer covering whatever needs to be covered more.)
Anyways, haha, put a few dots where you have problems and blend it out with a stippling brush, like the Cover FX #160 Cream Foundation Brush (pictured left), or a beautyblender beautyblender® sponge (pictured right).
Then, just set it all where you need to (don't apply foundation and powder all over, that can lead to a cakey face) with powder. I'd recommend Benefit Cosmetics Powderflage Set if you only need to apply it to a small area, as it is a little expensive. If you need to cover a large area, I'd look at CoverGirl powders.
Hope this helped, I've been dealing with blackheads for a while now so this is all from experience Good luck!
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I personally use two great products that have eliminated the blackheads. You don't want to clog your pores any more than necessary trying to cover them up. I use a clarisonic mia (if your skin is sensitive they have an appropriate brush), along with Perricone's glycolic cleansing bar and Pore Minimizer Toner. The results are absolutely amazing.