I would say write her a letter - they are so lovely to get when you're up to your eyeballs. I used to receive letters and had them in my dressing gown pockets to whip em out when I had a few seconds to read.
I think you are being a bit unreasonable as your friend is actually telling you something about what she needs from you at the moment, but you seem to not want to hear it and just want validation for yourself?
I would write her a letter. That way you'll hear from her if there really is something wrong, and if there's nothing wrong, you can rest at ease knowing that she's just too busy to contact you - nothing personal, she's had a baby.
As someone else posted, it's not all about you.
A new baby does give people the right to be a little bit rude - sleep deprivation is a known torture. The normal rules don't apply. I feel it's a wee bit self centered of you to think that she will wake herself up from a nap just to thank you for your unasked for gifts by text.
I wasn't able to do anything except the bare essentials for my babe in the first 6 months. Let alone things that I needed doing for myself, and my friends without kids / babies fell off the earth as far as I was concerned for the first year.
Write her a letter - she may have time to jot something down back, and may even have time to post it!