I'm on my second puker. I thought that I was going to dodge that bullet with this one, but the real puking just didn't set in until 3-4 weeks with her and now... watch out! They do eventually outgrow it... my 3 year old DD keeps her meals down now and she was the world's spittiest baby. My husband is a pedi and the way both he and DD1's old doctor explained it is that it's because the gastro-esophageal sphincter is more immature in some babies than others. In our case this is also aggravated by a very forceful letdown and babies who like to gulp and "overeat" (myth, you can't overfeed an EBF baby). In a baby who is happy and gaining well this really is "just a laundry problem." The medical solutions available all involve antacids and/or special formulas and often result in a baby who still spits up.
Honestly, I'm not sure that there's any choice other than to get really zen about it. My DH swears that it would improve if I would burp her in the MIDDLE of feedings (this is the advice for bottle fed babies), but in my experience that just results in an angry baby who still spits up.
My strategies for leaving the house:
x. Burp her until she pukes a decent amount (because you KNOW that it will be coming up at some point).
x. Hold her upright for 20 minutes or more after a feeding.
x. Turn her head to the side (like a passed out drunk) while changing her and be prepared to wipe puke before it can trickle down to her clothes.
x. Bibs. It is easier to change a bib than an entire outfit.
x. Strategically placed prefolds at all times if I don't want to change my outfit. Even this doesn't always work because she can puke with some force... but changing my shirt isn't as hard as changing hers.
x. I try to wait 30-60 minutes after feeding her to put her in her car seat... I couldn't do this with DD1 though because she was both a puker and a 24-7 cluster feeder.
Bibs really do catch a decent amount of spit-up and eliminate some outfit changes. And after months of it (or by your second baby with the same problem) you start to care less about cleanliness... or at least I did. If an outfit only has a little spit-up on it, I wipe it off... if it still feels reasonably dry and like it isn't going to irritate her skin I leave it on. I figure between the BIG pukes and the epic poop explosions (problem with DD2, never had this with the first) I'll be changing it sooner than later anyway.
I know that none of this is probably what you want to hear. In our case it seems that allergies are very unlikely to be the cause because when I finally introduced the common allergenic foods to DD1 she handled them perfectly fine.
My best advice? Hand the baby to your partner for a few hours every day and take the time to get clean, dry, and regain your sanity. If the baby can't go 90 minutes without eating an occasional bottle won't hurt once she's a few months old. (In my experience though even my every 45 minutes baby would rather hang out with daddy for an hour or two and wait for me rather than take a bottle.) I have also gotten into the habit of handing the baby to someone else if there is anyone at all available as SOON as she finishes eating and walking away to engage in a dry activity like putting away laundry.
Oh, and burping position doesn't seem to matter/help for my kids either. So my current strategy is to put a prefold over one leg and to lay Livia across my lap and occasionally pat her back/jiggle her with my legs until she pukes or starts fussing. The fussing usually indicates that she's a) ready to eat again b) ready to not puke c) ready to be upright for the express purpose of puking. I only mention this position because it's the easiest one in which to do other things (i.e. play online, read books) and makes it a little less boring.
For the record: I am SO jealous of mothers who can nurse their babies lying down from infancy... DD1 was several months (probably closer to 6) before she could handle this because of all the puking and it looks like DD2 is following in her footsteps.