I have not received a 1099 from the entities that I did business with in 2022, but I listed all of the income. Am I allowed to go ahead and file? Or wait for them?

Yes you don't need the 1099NEC .  Actually you can just enter it as Other self employment income or as Cash or General income.  You don't need to get a 1099NEC or 1099Misc or 1099K.  Even if you did you can enter all your income as Cash.  Only the total goes to schedule C.

Although your tax return may be correct if you don't enter all of your form 1099-NEC's, it may be wise to do so as the IRS may match them up with your return if you file it electronically. Then, if there is missing form 1099-NEC entries it may result in you getting a notice down the road from the IRS assessing tax for the income reported on the missing forms. You can straighten that out by explaning what happend, but by entering all of the 1099 forms you may avoid extra work down the road.