You sound like you have a really good shot. Most top colleges consider 3.7-3.8 competitive so your GPA is pretty impressive (especially with the classwork).
Just did a quick check, Rice admits 17% of transfers, USC admits 29%, UNC admits 39%, and Notre Dame admits 25%. I think you’re probably at the top of the pool. Just perfect your apps and you’ll probably get in to a couple of them.