As a fellow in a peds specialty, I can promise you this: You'll be able to get in somewhere, as a US Med student, that won't be an issue if you apply broadly enough. In the 2013 match only 43 out of 1826 US Seniors who ranked only pediatrics programs went unmatched (2.3%).
So long as you apply and interview broadly (go on as many interviews as you have time and can afford) and more importantly RANK as many programs as you consider acceptable (and in your case perhaps as many programs as superior to going unmatched), and you should be fine.
When applying, find as many programs as you can that fit your general criteria (freestanding children's hospital or not, program size, location, research considerations, etc), and apply to all that fit those criteria. Then, determine which criterion is not as important as the others and loosen that search for programs outside that ideal - maybe you don't really care that much about program size so you expand your search to include bigger or smaller programs that otherwise meet your ideals for everything else. Keep expanding those searches until you have all the programs that could possibly be an option and then see how it goes.
When it comes to ranking, the key consideration for peds is to make sure you rank enough programs. The 2011 match was the last time the NRMP did a full analysis on what get's participants matched, and number of contiguous ranked programs within the specialty is most important (ie spots 1-4 or 1-7) independent variable. Being able to rank a large number of programs means that you interviewed at a large number, which in more competitive specialties probably is more a marker of overall competitiveness as an applicant, but in Peds more likely means you applied to programs the right way. In 2011, the average matched US Senior ranked a mean number of 9.6 programs compared to 6.8 for unmatched US Seniors.
Bottom line, follow the advice that you always hear and you should be fine. Don't get fixated on one program, keep an open mind and it'll work out the way it's supposed to.
And you should probably stay away from voicing your matching concerns when talking to your friends trying for ENT/Ophtho/Derm/Ortho/Rads/etc, they might not appreciate it.
