I interpret your question to be
how can I deal with possibly being treated differently and/or with some hostility by American people while choosing to cover my head in public?
If that is not an accurate interpretation, please edit your question to clarify.
I am Indian and know (though people who are not very familiar with Asian religions and culture may not be aware) that covering the head in public for religious reasons is practiced by Middle Eastern, Southern Asian, African or American women and men belonging to at least 4 different religions -- let's not go into the details, to avoid potentially argumentative discussion unrelated to your situation, but covering the head is required of believers by multiple orthodox religions for different theological reasons.
However, perceptions of head-covering in the Western world have been shaped by both
the clash of religious ideologies and cultures between East and West, leading to the political 'war of terror' between fundamentalist fanatics and Western world governments; and
modern feminist discourse about the rights of women and their oppression by patriarchy,
for both of which head-covering is seen as a visible marker.
There is a pervasive idea (among men and women whose religions do not require head-covering) that this practice is imposed compulsorily on women by men, but many recent explanations by women who choose to cover their heads for religious reasons emphasise their free personal choice due to individual religious convictions, which they claim as an unalienable part of their right to practice their religion in a free society.
In short it is your fundamental right in a free society to cover your head if you want to, even if not for religious reasons, except where certain governments have legislated against the practice, but you need to be aware that just as you are entitled to your religious rights, so also individual persons and communities are (sad but true) 'entitled' to their religious and cultural prejudices, which it is not possible for anyone to change in a hurry, nor advisable for you to address as a non-native person in a Western country [if that description of your situation is not accurate, please edit your question to clarify.]
By choosing to do something that 'goes against the grain' of the prevailing culture and social expectations, you are choosing not to 'dissolve' into the local culture but to practise your religion conspicuously at risk of being treated differently and/or with hostility by the majority community, or else to give that impression to others, if you are not doing it for religious reasons. Whatever be your motive, it is your right but exposes you to social stress, and you know it. So you must be well prepared psychologically to deal with the backlash:
Always keep a positive (read confident) body language and an open yet neutral expression. This signals to strangers in public that your decision to cover your head is a fully voluntary personal choice and your attitude to people is still open and neutral.
Also be mentally prepared for some degree of unpleasantness and learn not to be badly affected by such incidents.
Do not engage in debate about head covering, although a friendly discussion is probably OK. If a 'friendly discussion' looks likely to become a debate, just stop the discussion yourself to avoid escalation.
Do not pick an argument with anybody who treats you differently or with hostility, because you should expect it. It is not useful for you to question their cultural attitudes in an argumentative manner. However, if anybody infringes any of your legitimate rights you are fully entitled to complain to the appropriate authorities.
If you actually fear that you will be harmed by a random person then you might reconsider your decision to cover your head in public.
Making friends in the neighborhood and at the workplace will help you understand American cultural expectations and simultaneously allow others to get an insight into your religion and culture. Having women friends in particular tends to empower a South Asian immigrant woman by cutting across cultural differences and emphasising the commonality and solidarity of women's experiences all over the world.
In general it is good to be in tune with the social and cultural expectations of the society you are living in, even as a non-native person, but would I give up being a vegetarian from birth for religious reasons, and eat meat simply to blend in? It cuts deep and creates internal conflict, but many immigrants have compromised their religious beliefs and practices to 'purchase peace' in a new place. It avoids a great deal of unpleasantness arising from ideological differences, misunderstanding and prejudice, and allows the person to concentrate on building their life and work. However, the greatness of the USA nation and society lies in allowing every person the fullest cultural freedom provided by the law, and I am sure you will soon learn to exercise your personal or religious rights in harmony with the local community.