COVID-19 has resulted in stress for everyone, counselors included. I am unable to do justice to some of my clients who need more sessions, because of my personal situations but they are not willing to be transferred to someone else. What do I do?

The client needs to be explained that the unwillingness to change is understandable. A possible solution to allay anxiety related to change of therapists is to have a one/few joint sessions with the new therapist and the client. Another possible way to deal with this situation is by involving another therapist in the care of the client. You can plan the therapy process along with the new therapist, with some sessions being covered by the new therapist and some by you. If this is not possible, then the only way is to clarify to the client about the time constraints, and not overburden yourself.