So I messed up really bad and cheated on a homework assignment. I got a negative one for that assignment. I'm in my first year of undergraduate school in the US, second semester. I am so upset with myself for stooping so low to commit academic dishonesty by looking into the solution manual. I'm terrified of what will happen to me. Since this is a relatively minor offense, what do you think will happen? Where do I go from here?
What will happen depends on your professor and school policy. Also on how you handled it- in general, if you admitted to cheating when confronted, you may be treated with more leniency than, say, you denied it and tried to pin the blame on something else. This is all quite subjective, and not really in your hands.
What is in your hands is what you do now. I suggest you make a formal apology, preferably written, to the professor and genuinely mean it. Beyond that, accept whatever punishment is given (unless it is clearly unfair or too harsh). As an undergraduate, this should not be something that will make a permanent blot on your career, but it is up to you and you alone, to work hard and notch up sufficient credit that this misdemeanor may be overlooked.