Hey there!
I've read just the first chapter only. I feel like you've got the voice down for the setting/era you've set the piece in. Can't say I've had much experience with pieces from that era, but it seemed natural enough. There were a few times where the dialogue could have been just slightly different to make it seem more so, but I can't copy/paste from Wattpad so I can't really tell you which parts specifically. It wasn't anything very serious, though, just things that maybe could be ameliorated.
Honestly, critiquing this is going to be a bit difficult and unfortunately vague. I usually enjoy taking parts of the pieces, quoting them here, and telling you my thoughts on them, but without being able to copy/paste into my reply, it's a little frustrating. Heh. I'm not about to just write out everything, so I guess I'll just give you general notes.
Clearly, grammar and spelling isn't a big issue for you. You've got that down, packed and solid. Your voice, as I've already said, is great. I've noticed a lot of authors having difficulty writing in first person because they often stick with "I said [...]" or "I did [...]" type sentence structures, but you've got a great flow and do a very good job of 'hiding the I' and making it a natural read.
There were some issues I spotted, though. You use the semi-colon ( ; ) quite a few times in just the chapter I read. While a few times it can be effective, when it's over-done it looks a little odd and reads a little oddly as well. I would suggest going through it and seeing what you can separate completely into two sentence (with a period) or reword things to make it all part of the sentence (with a comma), depending on what you'd rather.
Your style is lovely, your words spelled right, dialogue natural, but I just... didn't feel the pull in the first chapter. The first few pages of a novel are very important, because people will decide whether to keep reading or put it away and find something else. Though there was nothing blaringly wrong with your piece, as I've said, I don't think you gave the readers (or at the very least, me) a good reason to keep reading. The same initials and same birthday aren't intriguing enough if she just walks away at the end and nothing's really changed. He just goes back to his party and she's gone, and outside of the little quip his friend makes (his friend who is totally awesome, by the way. I'm a fan of Algernon hehe), it's just assumed that things go back to the way they were. I assume you meant the chapter to be an introductory tool, to show us who the characters are and all, but I didn't feel like enough happened to make me want to keep reading.
It's still got crazy potential, though, because it's clear in the way you write that you really know your characters. It's clear, too, that you've put a lot of thought into the setting (just with the names and little details like the hat and what people do for birthdays and how everyone's married and all). I would suggest maybe making an outline of the piece and a chapter outline, making sure that something changes/is altered/moves the story forward at each part/chapter you plan to write.
I'm going to give the second chapter a read once I've got a bit more time - maybe after work tonight. I know I keep mentioning the style/voice you write in, but it's really awesome and I'm really impressed - probably because I most likely couldn't manage something like that. It's a good piece with great potential! Good luck finishing it!