Hi!
If done deep cleaning means the deposits would have been deep. You need to go on regular timed appointments as advised by your dentist who will c the progress of the treatment done.
The gaps that you see are normal and has to be there which will help in self cleansing procedure.
If you find your gums are swollen for a longer duration then you should visit a dentist for clinical evaluation and advise.
Next Steps
Visit a dentist and clear off the doubts and proceed with the treatment.
Health Tips
Don't adjust with any abnormal/ different condition for more than a week. Better to meet a dentist and clear off the doubts. Take care.