Hello! In my opinion, "as I've got older" refers to the physical process of getting older each year and has a direct connection to physical age. "as I've grown up" refers to the person's mental or emotional development meaning they have learnt from life and have become more world-wise or become more experienced in life itself; "to grow up" doesn't necessarily have a particular time frame - it could happen over a few months or a few years, but "to get older" definitely happens after each birthday of each year.

Wow. I totally get it. Thanks<3

My immediate reaction is that "as I've got older" and "as I've grown up" are basically the same, although there is a slight difference in emphasis - "grown up" implies you've acquired more wisdom, whereas "got older" doesn't, eg. "As I've got older I've got less tolerant of noise" (just a comment on the effects of ageing) "As I've grown up I've become more interested in exotic food" (implying very slightly that it's good to be interested in exotic food) The other big difference is that I don't think anyone over the age of about 25 would use "as I've grown up", as it really refers to becoming an adult. "As I've got older" is normally used by older adults. "When I'm grown up" (not "I've") or "when I grow up" is an extremely common phrase used by children. "When I'm grown up, I'm going to eat sweets for every meal". "After I've grown up" is grammatical but isn't used; "After grown up" isn't grammatical.