Do formula fed babies sleep longer then breastfed babies i am breastfeeding its effecting me mentally ?

At just 3 weeks old - it really doesn't matter if it is breast milk or formula.  The baby is still going to wake for a feeding very often.  They just can't take in enough to stay satisfied for very long because their tummies are just too small.   If breast milk is being given every two to three hours - changing to formula MIGHT extend that to be every three to four hours.  It doesn't really make a big difference.

If you are going to try formula once per day - then use the formula for one of the night time feedings - either the first bed time feeding or one of the middle of the night feedings.  This MIGHT create one time frame in which the baby sleeps just a little longer before needing the next feeding.  If you go to bed right after feeding the formula - it might let you get a little extra rest too.

Feeding formula during the daytime hours won't cause the baby to sleep better at night.  Feeding them something that digests a little slower at the point they are ready to  sleep might help them sleep longer before becoming hungry again.  

BTW - both of my babies were given formula only.  My first baby usually wanted to eat about every three hours until around six weeks old and then it stretched out to more of every four to five hours.  My second baby demanded food every two hours but would only drink about two ounces each time.  It was impossible to get her to take more at one time to try to satisfy her longer.  This pattern lasted until she was about four weeks old and she finally started drinking more at one time and going longer between feedings.  (but it was a very tiring first month - especially with having another child to care for too.)

Good luck.

I read that is true so I tried it for my baby but she still woke up every 2 or 3 hours to eat. I had to substitute because my milk supply was getting low. I think for some babies it might. Keep in mind breast milk digest faster. Your baby might be puking because she's not being burped, happened with my baby. 

Not necessarily.  Talk to your ob/gyn and your pediatrician.  Many babies will not go back and forth between breast and bottle. If you start bottle feeding you may find your baby will refuse the breast and you'll end up pumping and feeding in a bottle.

Every mother is exhausted and at her wits end at 3 weeks.  Your options include:

1. Get some help.  Have a friend, family member, or hired caregiver come in to give you a break so you can sleep and take a shower.

2. Get your pediatrician to help figure out why your child is constantly puking.  All baby throw up an burb up milk, but if your child is vomiting all her food, she should be seen by her doctor asap.