You can go to the clerk in the family court and ask to file a motion. The staff will walk you through the procedure. You can file a motion for an increase only if your spouse's circumstances have changed dramatically in that s/he can now afford to pay more.
You should go back to the lawyer who got you the child support in the first place. They will help you file the motion to get more child support. You need good proof that you need more money. They will go by what your ex can afford too.
You would have to go to court and file papers showing proof that either you are aware that the other party has received a salary increase, which would allow them to pay more, or t hat the children's needs have increased, which requires a larger support payment from the other party.
If the person paying the child support did not get an increase in household income then most likely the judge will make you responsible for the difference.
Child support is not based on your need, but is based on a percentage of each person income. This is independent of what the other person makes. If the person you are receiving child support from has not increased in income you will not get an increase. If they have there are organization that can help you file.
You file a motion to increase child support and you'll prove that your income is not sufficient to support your children on the amount of child support you get. You'll also have to speak with your lawyer if the father refuses to appear in court. You may want to a spokesperson.