Yes you most likely are not fully recovered. If your doing pull ups 3 times a week aiming to improve them then you shouldn't exert to failure often. It will cause this issue.

If your max is 16. Do 8. Do 3-5 sets of 8. Rest long, 5 minutes is sufficient but more would be better. You will hit 8 every set. Repeat 3 times a week. Once this becomes easy, not comfortable, but easy. Move to 10. Then 12. But I stress, easy, not comfortable before upping reps. You dont want or need a burn to improve.

The benefit to this is you will be recovered and you will be confident; not stressed or worried about meeting your target. After maybe 4 weeks try a new max. It will be higher. Hell I went from a max of 14 to 23 in 3 weeks doing just this.