Hi...
To start with we need to know when was this x-ray taken before you got your cleaning done or after that.
Your medical history if any like many systemic diseases cause bone loss like
diabetes etc.
If this x-ray was taken before cleaning then you have bone loss and pockets around those areas which can be treated with scaling and root planing/ flap surgery along with medications (preferably from a periodontist).
But as you have mentioned that the pain started after cleaning, go visit your dentist again and if you are not very confident that treatment was carried out very well then please go for a second opinion.
Next Steps
Consult a dentist online/offline
Health Tips
Try brushing twice daily
Do warm saline rinses twice daily and massage your gums with finger gently for 3-4 days