Maybe she is saving it to read again later, perhaps thinking about a response. Reading a little about your sitch, maybe the "falling in love comment" might be too strong. I don't think it's a bad thing. I would be patient for a bit and see what happens.

I think the letter which you sent was a very good idea.

If/when you guys go on a second date in the weeks to come (likely you will), after the date, if it goes well (it should) go to a card shop or somewhere that sells the cute little stuffed animals, get a small cute one. Box it up and send it with a very tiny card or tag, that reads "you're cute" or "you're sweet". Wait a few days and see if she responds.

She can then display this and be reminded of you, without any fear that someone else sees it and asks questions. Whereas a card with your name on it, might get hidden.

I think the "soft sell" might work for you

IS 49 W 47 S 21 D 19 S 16
M 24y Together 31y
EA Mar04-May 06
PA Feb06-Jun06 EA May07
Bomb Dec 28 07

Footfalls echo in the memory, down the passage which we did not take, towards the door we never opened Into the rose-garden.
T. S. Eliot