That's a really good question. I guess the answer is, it feels normal. Because it feels normal to them, and so if you are that person, then feeling like they do feels normal to you. But what we really want to know is, how would it feel for me to feel what they are feeling? If I could "see" what a red apple looked like to them, would it look red to me? Or would it look green? If I could feel their sleepiness, would it feel like mine? Fortunately, Milo, philosophers have thought long and hard about this question. Unfortunately, we haven't figured it out yet. What do you think?
What makes me the same person today as I was any time in the past? I have new memories and experiences, so why aren't I someone else?
You have changed. But for anything to change, it has to still be there after the change--otherwise how can it differ from how it was? In our jargon, you differ qualitatively ---you have different features from before---but you are the same numerically ---you are the very individual who existed in the past. Puzzle: is the gain or loss of the feature of existing (when something comes or ceases to be) a change? Can something gain or lose that feature?
I imagine that you've put on a few pounds since then, but you gave the game away with the word "I". You can only use that word to refer to one person, namely yourself. So if there is any person you can describe as "the person I was when I was two", it's the same person as the one you can describe as "the person I am today". If you want to leave open the question whether a single person has persisted over time occupying the body that you now inhabit, ask it...well, that way. I'm guessing the answer to that one is also yes, unless you're the sort that sends yourselves birthday cards.