That sounds like baby reflux to me!
My LO would projectile vomit about 3-5 times a day. It could be 5 minutes after eating or an hour. It was awful.
As PP mentioned about the clear liquid, that's most likely acid from their stomach being empty when they vomit.
They should probably be on something to stop the acid from forming, like Prilosec or Prevacid (PPI-Proton Pump Inhibitors) or Zantac, which blocks the acid. Usually they start with Zantac, of that doesn't work they go to a PPI.
And yes, laying your baby down flat is the worst thing for reflux. Here are some tips I've learned along to way:
1. Keep baby upright for about 30 minutes after feeds. That helps the acid to not come back up and hurt.
2. Invest in a crib wedge so they can sleep on a 45 degree angle. We use a "Nap Nanny." She sleeps really well in it and it keeps her inclined for comfort.
3. Milk protein/soy allergies and reflux go hand in hand, so you may want to try switching their formula for something hypoallergienic, like Enfamil Nutramigen, Similac Alimentum, Neocate, or Elecare. Neocate and Elecare are better choices as the proteins are broken down more than with the Alimentum or Nutramigen. Warning: They all stink, so don't be surprised if they hate it at first.
4. Always give them their medication (Zantac or Prilosec/Prevacid) on an empty stomach as it works much better that way, and make sure they are getting the full dose. It takes a few weeks to really see a difference, but just be patient.
5. You can thicken feeds with rice cereal to help it stay down better. But if your LO does have the allergy, make sure there is no soy in the rice cereal you're using (I learned that the hard way). Beechnut makes theirs soy free. Gerber rice cereal has soy in it.
6. Laying them on their side helps a lot too. We've found this to be the best for our little girl. Always on the right side as that will usually stop their stomach from emptying and it relieves the reflux.
7. For bad gas, you can give them a probiotic in their formula. We use one called "Flora Baby." It's organic and it's in powdered form. Once a day does the trick. If you end up switching the formula to hypoallergenic, the Nutramigen has a probiotic in it, but if your LO likes their bottles warm, it will cause the probiotic to not work, so you would still need to use the extra probiotic if you warm the bottles.
I hope these tips work for you ladies. My daughter takes Zantac twice a day (we tried Prilosec, which is the stronger medication but she gagged and vomited everytime we gave it to her) and is also on Similac Alimentum. She is a completely different baby now. She's actually happy, she eats more because she's not in as much pain, she doesn't power vomit at all. It's like a complete 180 degrees from where she was when we first started this journey.
Good luck. I hope your LO's grow out of the reflux soon!!