Is there anything wrong with saying "I was feeling amazing at the party with all my friends around"? Is it grammatically incorrect? Should this be said some other way?
It's important to note that many people use "amazing" as slang to mean "very good," "awesome," "excellent" etc. But other forms of the verb "amaze" are taken literally.
So your two sentences are both grammatical, but have different meanings because of the colloquial meaning of "amazing"
I was feeling amazing at the party ...
means that you were feeling exceptionally good while at the party. The party likely put you in high spirits.
I was feeling amazed at the party...
means that you literally were amazed while at the party. Perhaps the party was a lot better than you expected, and you were impressed by the quality. Or maybe you were amazed by a illusionist/magic show.
I was feeling amazing at the party with all my friends.
I was feeling amazed at the party with all my friends.
You usually use the adjective amazing like many other adjectives ending with "ing" to express the characteristic of somebody or something such as:
His performance was quite amazing.
He is an amazing player.
The meal was amazing.
In these sentences, the amazing means very surprising. In spoken English, it also means great, wonderful.
I think the adjective amazing in the sentence I was feeling amazing has been used in the latter sense that I was feeling very good/great at the party.
As for the adjective amazed like many adjectives ending with "ed", it's used to express a feeting, The adjective amazed means extremely surprised. So the sentence means that I was feeling extremely surprised at the party.