I also had heat damage from flat ironing for 4 years. protein treatments have really helped me get curl back. Even after I'd cut all the heat damage hair it still wouldn't curl right (more than before, but not w/a consistent curl pattern).
Also a baby picture that young may not tell you your hair texture at all. My younger siblings were both born with bone straight hair. My brothers started to curl within months and he was probably a 4a/b by the time he was one. My sister's took longer to curl and at 2 yrs old she is moving from 2's to 3's, but my mom always says her hair is how mine was at that age and I think I am 3c 4a/b mixture now (18 yrs old), so who knows what she will end up with? It can takes years for your hair to change.
If you have the kind of heat damage you say, and your hair is in the 3's now, it probably move into 4's once the damage parts are gone and you take care of it.