Once your rescue dog feels welcome home, (s)he will often show you affection. Rescue dogs show their affection more than non-rescue dogs. And they seek more affection too! Or should we say, they need more affection?
Not all but many rescue dogs have suffered quite a bit in the past: Possibly under their prior owner, possibly hunger, thirst, bladder and bowel pressure. And probably from lack of affection. They felt lonely or even left alone. Lost or even forgotten. Misplaced or even unwanted.
Now that you have rescued the dog, (s)he has new hope. And you have the unique opportunity to make your rescue dog feel home and belonging to your family. Feeling welcome and wanted. What a difference for your dog! This is why rescue dogs generally show their affection more than non-rescue dogs.
But now comes where many dog owners go wrong (particularly but not only new dog owners). They return the dog's affection with our human signals of affection: Hugging, kissing on face or head, even headlocking. None of this dogs like as you will know when you can read their body language, and here we don't need to add generally.
While many dogs, all the more grateful rescue dogs, will accept if you do any of that, no dog likes that. Because hugging, kissing on face or head, and headlocking all are against the dog's nature and survival instinct.
Where we people use our hands to free us, to protect us, to greet, to show gratitude etc, dogs use their mouth because their front feet are genetically "grounded" (not developed for anything but running on firm ground).
Now when you hug your dog, kiss on face or head, or even headlock the dog, the mouth and head aren't free to move, and so the dog must feel like you would feel if I tied your hands behind your back. I won't do that, don't you worry. But would that make you feel good?
No. And neither the dog, whether rescue or not.
Instead of showing affection in human ways, with our dog (or another dog) we should show affection in canine ways. In ways dogs do, and dogs like. Clearly dogs would do the same for us - if only they could with their paws.
But not all dogs are the same. So why not try this: Try to consciously observe how your rescue dog shows affection. Then take note. Maybe some of these ways of showing affection you can and want to replicate, while others probably not.
Note that every key point raised above you can find more comprehensively explained in other places on this website. The menu is your friend. Here, links have been omitted only to keep this decision tree straightforward.
PLEASE NOTE: Posting a fragment of your overall dog problem in the comments below is not going to help. Provide complete details if you really seek the right solution. Of course we have a page for that as well: Dog Problem Consultation.