I agree. Tell them that due to your medical problems which includes the pain medication after surgery that you will be unable to complete their projects till at least the end of the year and possibly into next year. Your family and friends should understand. If they don't then consider whether you should be knitting for them at all.
Charity projects do sometimes have due dates for various reasons, but it's likely you're not the only one knitting for them. Tell them the same thing and if they need them by a certain time you'll just have to tell them you won't be able to do this project. Maybe next time.
I have arthritis in my spine at the cervical level. Unfortunately they cant replace that.
I hope you feel better soon!