Absolutely! Though I actually heard a young man get up in court regarding child support and announce that he was self employed and then explain he gambled on the internet! Self employed does sound lots better than "working under the table" which is a famous dodge for paying child support obligations.
But also, reframe how "she didn't ask for child support because we were getting along at that time." The court will assume this: When you have a child, you are always going to have child support obligations of some kind or another. Whether you are sharing custody of the child, keeping the child 100% of the time, having visitation, or never seeing the child, there is always SOMEONE supporting that child. If there are two parents, this reponsibility should be shared.
if there is no court determined amount to be paid, no formally established rule to follow, then it paves the way for many years of sheer misery and on going bitterness and battles. That how much is paid and to whom is due to your whim or her demands that any support at all is given, that no records are kept (she could go back and say you never gave her a penny even when you had) It is bad for both of you and for the child. Not to mention anyone else who is in a relationship with you, as there will be continuous drama with whether or not we have to give that person money and how much and when.
I suppose the idea was that if she needed money she'd just ask. Or that you'd pay what you could when you could. Or that you'd take the child, though I do not for the life of me see how you can maintain work of the type you do and raise this child without a very good income and very good child care. I don't care what a prize your next girlfriend is, she could leave, and leave you holding the bag on child care in a heartbeat, even if you had sole custody. This has been dragging on for a long time, no one in the court system is going to believe that you would be able to have joint or full custody of your son unless you have demonstrated you are responsible enough to get through the legal processes without undue drama and set up custody and visitation arrangments. And that you are self supporting, and can support the child.
Instead of going back to court to try to get your obligation lowered right now, work on getting to a position where you can meet those obligations, and then begin to work on visitation arrangements.