It's unlikely. If you were arrested, held and released, and they told you that they may pick them up later, it just means that you should stay out of trouble for the next year or so. And not sue them for false arrest. If you get in trouble again, or try and sue for false arrest, they'll go ahead and charge you. Other than that, you should be okay.
ADDED: Since the decision to charge or not to charge does not rest with either the complainant or the police, it is likely that the prosecutor filed a Nolle Prosequi in your case. Just because they declined to prosecute this particular offense does not mean that they cannot pick up the charge again at a later date (e.g.: if you assaulted the same person again - or, you make a habit of going around assaulting people), however, under normal circumstances, re-instituting the charge is highly unlikely.
If you were charged with a felony assault and the charges were dropped, you do not have a criminal record. The charges can be picked up by the state at a later date.
Depends on your state laws and many other factors. Consult a lawyer.
YOU cannot have the charges dropped by yourself. Such an assault is a crime against the state and only the prosecutor can 'drop' the charges. If you are a reluctant 'complaining witness' speak to the prosecutor about your hesitation to go forward.
state can pick up the charge if they want.
An assault case in the UK is The State vs The Accused, and while charges can be dropped at the request of the victim, it's not automatic. Depending on the circumstances (if the attacker was armed, whether the attack was premeditated) the state might ignore the wishes of the victim.
Sometimes charges can be dropped against someone even after an affidavit has been signed. It will really depend on the charges and city and state.
what is the difference between 1st, 2nd,and 3rd degree assault
It depends on the state. Some do not allow "assault on assault" charges.
It means exactly what it says. The State might have dropped charges because of lack of cooperation from the child's mother/custodian, because genetic testing showed that the male was not the child's father, or for other reason(s).
if they want to
Depending on the wording of the statutes in your particular state, the charges will be similar to: "Assault And Battery" - "Threats In A Menacing Manner" - Assault With A Deadly Weapon." If any injuries were suffered by the victim the charges could be 'enhanced.' When you are presented to court, you will be read the charges against you, and you will have the opportunity to consult with an attorney/public defender before you make your plea.
One way to file assault charges in the state of Virginia is to have police officer come to your home. A person can also visit the local courthouse and press charges there.