A "high level of testosterone" must be made within the context of a particular sex. Men tend to have much higher levels of testosterone than women, but the testosterone production and levels within women vary widely - just as many hormones. Genetics, environment, diet, drugs, and workout regimes can all affect testosterone levels. A qualified physician will be able to tell where a person is after a test.
As for the rest... Every case of gender reassignment I've heard of and read about has occurred after birth. Read through this Johns Hopkins Magazine article from Sept. 2000 to get a fairly good understanding of when gender reassignment occurs and how it's handled. Here's a quick rundown (summaries, NOT quotes from the article):
Inadequate exposure to Testosterone in utero can result in ambiguous genitalia or other conditions such as 'micropenis' for an XY fetus. Up until the 1990's, regardless of chromosomal gender, children with the conditions would be reassigned as 'female' and had reconstructive surgery very early on.
Androgen Insensitivity is when an XY fetus is genetically incapable of utilizing male hormones and can involve several levels of insensitivity from "Complete" to "Partial". Complete insensitivity usually leads to fully feminine genitalia, while "Mild" or "Partial" can lead to partially or fully masculinized genitalia. Genitoplasty is an option for the latter cases.
CAH - congenital adrenal hyperplasia. This genetic disease causes the adrenal glands to produce excess androgens--the steroids that cause masculinization--a process that begins in the womb and can result in ambiguous genitals. However, CAH girls are generally more aggressive and display behavioral tendencies that more closely coincide with boys of the same age. Important to note: CAH children are genetically female (XX) and identify as female.
An extensive review of gender reassignments in 1997 had this to say about the consequences of surgically altering an infant's sex:
Considering this case follow-up, and as far as an extensive literature review can attest, there is no known case where a 46 chromosome, XY male, unequivocally so at birth, has ever easily and fully accepted an imposed life as an androphilic female regardless of the physical and medical intervention.
HOWEVER - as with all things scientific - there is dissent from the Johns Hopkins article above:
Preliminary analysis of the data, says Migeon, indicates that almost all of the patients are content with the gender in which they were raised. All but two showed a gender identity and gender role in accordance with their gender of rearing.
There is significant divergence that has not been reconciled in any trustworthy article I could find. The modern practice is to raise the child as their genetic sex unless significantly afflicted.
In adult transgender individuals, things like Hormone Replacement Therapy are part of a regime - along with surgery, acclimatization courses, and psychological evaluations - that can successfully result in a person presenting themselves and physically resembling another sex.
With adequate surgery, hormone therapy, and proper treatment all-around, it is practically impossible to tell whether a person is transgender without getting invasive or performing genetic tests.
As with all things that veer into a hazy area between medical knowledge (medical advice is not allowed on this website) and human biology: DO NOT use the above information to diagnose yourself or anybody you know. ONLY a qualified medical professional can perform the necessary tests required and give a qualified interpretation of the results.