Personally I wouldn't bother, you will hear a million stories were people said it helped for them, and you never hear the stories were it didn't help.
Here in the uk, rice in bottles is stated a choking hazard, weaning is advised to begin at 6 months (pr the very minimum 4 months). Personally I would go to your doctor and seek advice. There is absolutely no need for food in such a young babies system at that age imo. My baby girl (aka velcro baby), was sick after a couple of feeds per day, had a crappy weight gain in the first 4 months, slept horrifically and it was hard going (we do bottle feed), it was tough.... but... she is fine, the sick was mainly due to her being bad with her wind, so she would burp and bring everything back up (complete projectile vomiting), is it after every feed or just the formula bottle? I don't know much about breastfeeding, but if it is every feed could it be something your eating possibly that is making him sick? Dairy intolenrences as such?! Is baby gaining weight as expected?
And sleep..... meh welcome to parenthood!!! DD still wakes once a night.. and is up for the day at 5am.... I think I will forever be tired