Can I file taxes as a barber with no license

What country?
In the US, the IRS is happy to take your money without a license for any business. They don't check.
I don't think the states check either.
But you are in a heap of other trouble practicing without a license, so what is the purpose of this?

You HAVE to file a tax return if you received income.

In many areas, hair care professionals do need to be licensed. But you need to check the rules where you live (or practice).