Disclaimer: I have no medical qualifications whatsoever and only have my own personal experience and random layperson knowledge to go on.
There's different sorts of anxiety medications that are used in different ways, which have different drawbacks and benefits.
It sounds like WheelofLife was given some kind of benzodiazepine like diazepam/Valium, which works really well in the very short term but you absolutely have to keep it short term otherwise you'll get dependent on it, and coming off it is horrendous (I used to know a guy who was quitting a diazepam habit and a heroin habit at the same time, and he said he found the diazepam way more difficult). Even if you can persuade a doctor to prescribe it, they generally won't give you enough for more than two weeks, and to be honest, I feel even that's too long. I use them personally for extreme, very time-limited symptoms, and they work really well, but I'm very careful not to take them consistently caused I don't want to experience what Wheel was unlucky enough to go through.
A couple of people have mentioned citalopram and sertraline, and there's a whole group of SSRI and similar medications like those which can help anxiety, but you have to take those every day rather than as-and-when. Also people tend to feel crappy with side effects for at least the first couple of weeks, and they usually don't start to help your anxiety until a few more weeks after that. Occasionally people get withdrawal effects when they eventually decide to come off them, but unlike the benzos that's a minority of people. I've been on a few SSRIs and never really had noticeable withdrawal symptoms (but then they didn't do much for me in the first place).
The other main one you might be offered is a beta-blocker like propranolol, which works by stopping the physical effects of anxiety. I think the idea is that if you're not shaking and sweaty and your heart isn't running a mile a minute, you'll feel calmer and be able to break the cycle of mental and physical anxiety symptoms feeding into each other. Personally I have no idea how well this works; I stopped taking it because it dropped my blood pressure so low I fainted every time I stood up. But I have friends who do really well on it. It starts working straight away, you can take it every day or just as and when, and you won't get nasty withdrawal effects like you do with benzos.
There are other medications used for anxiety but that tends to be further down the line.
My views on anxiety medication is that if you think it could help, the doctor thinks it could help, and you both think the potential benefits outweigh the risks, then they're a useful tool and can even help you engage with therapy to tackle your anxiety from another angle, but be aware of the possible downsides, and please God don't get a daily benzo habit. I don't know anything about breastfeeding and anxiety meds, though.