Lyric - from one woman to another,
It sounds like you are doing what I did before OCS (way back) and trying to be prepared. Good job, and don't give up. BUT I want you to be ready for a shock. I am 5 feet tall and in decent shape. I got a personal trainer when I joined up and by the time I got to OCS, I had worked up to a 12:30 mile and half. Although this was within passing, it was so much slower than the majority of the class that I ended up working my ass off for the next 13 weeks. For the first 9 weeks, it was pretty rough. I'm not telling you this to dissuade you; only to prepare you. It may be the most physically tasking 13 weeks of your life, but it will be worth it. The most important thing is that you keep TRYING. When it comes to push-ups, if you are having a hard time, just put your butt in the air and make an upside-down V. DO NOT let your knees drop or you will never hear the end of it. For the runs, just try your best and don't willingly get in the following van - I would fall out of runs all the time in the beginning, but I was trying my damnedest and they knew it. A few times they made me get in the van because my 5'0' legs just couldn't keep up with the 6"3" guy setting the pace, as hard as I tried. Your positive attitude and perseverence will show and make a big difference.
Someone mentioned SWO, with good reason. If they tell you that you have to go SWO, strongly question that statement and do your research. As an aviator, I am a bit biased, but the SWO community can be a tough one unless you're a workaholic who doesn't need much sleep. (C'mon, SWOs, you know it's true.)
My little brother is an enlisted Army National Guardsman; we poke fun at each other, and he salutes me, but it's all good. Don't worry, you and your brothers will be fine.
Being a female Naval Officer for 6 years has been a very interesting experience - if you have any more questions, please let me know and I'd be happy to help.
ODB