Joe, I'm going to be pretty straight with you, here.
The "circumstances" aren't determining your behaviour. You are both, every time you don't use condoms properly and consistently, making an ACTIVE CHOICE to take the risks that are causing you this stress.
You have every possible ability to make different choices: you're simply choosing otherwise.
We also ALL, even with through-the-roof chemistry, have the power to make choices with the sex we're having, and so long as no one is forcing or coercing us into something, with the sex we are all having, it is exactly what we are choosing to do.
If her OB/GYN is saying that the pill or other hormonal methods aren't right for her, there is likely a very sound reason for that. By all means, she can seek out a second opinion if she wants to be on the pill and feels that doctor made his or her detrmination about the pill based on anything other than her individual health issues. You didn't say anything here about why her doctor denied her the pill, so I can only presume it was because that doctor felt there were undue risks for her with the pill.
Too, there are other options -- if hormonal methods aren't okay for her, she could use a diaphragm, for instance, and those can be put in in advance of sex -- but again, ANY of these options mean that one or both of you needs to be making smart choices. I have yet to meet any comprehensive sex educator who wasn't in the job in part because we know full well how awesome sex can be: I can't think of a one of us I know who hasn't experienced chemistry that knocks the wind out of our lungs at least once. So, I get it: sometimes, sexual feelings scramble your brains.
But I also know full well they don't scramble them so much that choices aren't still active choices.
That said -- it's important regardless -- condoms really can't be considered to be at their maximum effectiveness when not used properly, and that means from start to finish, always. That means effective with both pregnancy prevention and STI protection.
Mind, it is thought to be unlikely for pre-ejaculate to contain sperm if a man has recently urinated. (But this has no impact when it comes to STIs: pre-ejaculate can carry the same viruses and parasites full ejaculate can.) On the other hand, withdrawal fails often, and sometimes one ejaculates faster than one is expecting. Beyond all of that, this has you stressed out, which makes taking these risks again and again plain old silly. The fact that anyone who absolutely does not want to become pregnant, or get someone else pregnant NEEDS to be using a reliable method of birth control properly, and you state you and your partner are such people, makes all this mishegoss just plain foolish. If you do not want a pregnancy, you've got to use a method of birth control, every time, and use it properly.
(And let's face it, when you're really using condoms right, the reducation of sensation is pretty minimal, far more so than most women's difference in sexual experience on the pill. I've had plenty of great minutes of sex in my life, but I can't think of even one single minute that's worth a month of worry, to the point of hair loss.)
So, for the time being, I'd suggest sticking with the condoms, and using them properly. That means putting them on before ANY genital contact, every single time. Sit down with your partner and make clear that YOU are committed to doing this (sometimes female partners have a much harder time setting limits when they get the impression their male partners aren't supporting them), and expect her to be just as committed. Make sure you both always each have a stash of condoms, and when the clothes start coming off, put in on the pillow. If you're not using lube with your condoms -- that's a drop or two inside, and then plenty on the outside -- to keep them feeling as great as they can, start doing that. If the condoms you're using aren't feeling so hot, experiment with some new sizes, styles and brands. But commit to this: if you can committ a whole life to a person, this is a cakewalk.
This is being a grownup. I don't say that to be a big jerk, but just as a point of fact. You're 24 (I have no idea how old your partner is): you can do this, and it is EASY. And the hard truth is, that if anyone really feels they cannot control their actions when it comes to sex, that's a person I'd not advise should be having sex with someone, period, because that person just ain't safe.
But I don't think you're that person: I think you can take charge of yourself better and can make smarter choices, the kind that are absolutely no big deal to do, but a really big deal when it comes to your sanity and what you both want for your lives.
So, step it up, Joe: you can do this.