The reason you probably feel comfortable and OK with a counselor compared to how you feel in general social situations, is because you know, in advance, what the parameters/limits of your interaction with the counselor are. And since you are Ok with these and accept these, again in advance before your appointment, you do not ever feel anxious or stressed, or feel the way you feel when you are in open ended social situations. You probably feel OK too, with non-personal social interactions, like the check out clerk at the grocery store, or meeting with a doctor, going to some official place, etc.
With SA, people are perpetually guarding themselves against perceived negative experiences/opinions/criticisms when they are with other people - you don’t know who will say/do what or when and thus, how can you protect yourself. This is a key and common element with SA.
Your perception that “I am not experiencing what other people experience in social situations” is just that - a perception. You have probably become over analytical about this, and this may have increased the perceived experience of you being treated differently.
The root cause of SA is what thoughts/stories a person chooses to keep in their mind, about themselves and other people. Thoughts include beliefs, opinions, fears, worries, imagined things, fantasy. None of these are true or real, but they seem that they are because the mind does not know the difference between a real thing and one that is not. All unreal things (those things which only exist in our mind) are not true by the way, ever.
A large percentage of people go through what a person with SA goes through, only in a much smaller/milder way and not to the extent that it affects their lives or makes them change what they may have wanted to do. The overwhelming majority of the world’s population still want to be accepted/liked, and worry about how they look, talk, dress, etc., but they are much less affected by rejection, indifference, not having friends/partners than people with SA are affected.
You may also be trying too hard to make yourself acceptable to others, instead of being natural and letting things go and come, as they will. You may not actually need to have any or much social interaction. Its not actually true that everyone is social and needs to have friends and a partner. Some people want/like to have that but there is huge variance in this (as there is in how much/with who, etc) but this variance is not allowed to manifest in society.
And if you are perhaps trying to "mold" yourself on what you think other people want, I can tell you this is a fruitless endeavor. How someone gets to any one opinion they have is 100% unknown, even to the person who holds it. Secondly, opinions are constantly changing and person A can decide, in any moment, that what they opined about 1 hour ago has now changed.
So, how are you going to keep up with these two unknowable things, perpetually? Thus it is impossible to try to get acceptance from others because of what you do/say, even if you knew what people wanted/liked, which you won't ever, as even the other people don't actually know why they like what they do.
Lastly, the number of people you have experienced the social situations that you have is probably very small and some may even be the same people, over and over. There are 7.5 billion people on the planet - why worry about what an unmeasurable minuscule % of them think or feel about you?
There will always be people who will like you and will not like you - this is something you will never ever have any control over nor can you affect it in any way.
But you don't have to care or worry about either, because the truth is that you (and everyone) can be quite fine, whether someone likes you or not, wants to be your friend or not, thinks you're cool or not, thinks you're funny or not, etc.
But being natural is probably not possible while you harbor untruths about yourself and others in your mind. So I would think you would benefit from learning about what SA is and how you can overcome it, which I did about 5 years ago.
I can tell you more if you want, so PM me if you’d like.