Nostalgia is a noun, so we don't use that with "I feel." You would use the adjective, "nostalgic." For example, you say, "I feel happy." Happy is an adjective. You wouldn't say, "I feel happiness," as happiness is a noun. If you want to use the word "nostalgia," then you would need to put something like, "This gives me a sense of nostalgia." "Sense of nostalgia" is a common collocation, meaning words or phrases commonly used together. Hope that makes sense and is helpful.

They mean the same thing.. it’s more common I think to stay “I feel nostalgic” in the adjective form but “to feel nostalgia” is the same idea and not incorrect depending on the context.. it just feels a bit more formal/uncommon than the adjective “nostalgic” in my opinion. For example: I feel so nostalgic when I smell apple pie. I feel a lot of nostalgia at the bakery. Both are correct. Or you could say: Apple pie always gives me nostalgia. Apple pie always makes me nostalgic. Another word that can sort of do this, as another example, is grief or grieved. Grief is the noun and grieved is the adjective. For example: I feel so much grief when I watch the news. I feel grieved every time I watch the news. They both work and are proper English. Hope that helps. :)

Nostalgia is a noun, so the phrase doesn't make sense. I feel nostalgic - the adjective describing how you feel.