I've been feeding my newborn milk left out for more than two hours?

My mom was supposed to help me with taking care of my newborn as I haven't really a clue what I'm doing. He's 11 days old and he has vomited twice in that time and I got curious and looked up about his feeding habits. My mom had me believe it was OK to boil the kettle, fill 3 or 4 bottles with water and... show more My mom was supposed to help me with taking care of my newborn as I haven't really a clue what I'm doing. He's 11 days old and he has vomited twice in that time and I got curious and looked up about his feeding habits. My mom had me believe it was OK to boil the kettle, fill 3 or 4 bottles with water and add the formula to the water whenever he wanted a bottle the water would be left to cool for at least 3 or 4 hours sometimes all night and then I would add the formula when he wakes and I would feed him with that. I just read online that you add the formula to the boiled water and then leave it cool and you don't use milk past 2 hours old. I had also been leaving the ends of bottles and giving him the rest when he would wake. I'm obviously not going to be doing this anymore but now I'm freaking out is he going to be OK. He's acted fine the whole time just the two times he threw up. Please should I bring him to the hospital or will it be OK once I start feeding him properly. I feel like such an idiot I don't know why I took my moms word for it, I should have read the directions and everything I just thought she would know best.
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