Questions: Family & Friends

Should I text this to my friend? So my friend has been acting a bit distant lately (takes a long time to reply, like 1, 2 or 3 days, she even left me on read once, etc). She apologized on her own for being inactive and not feeling good as well (well I think that's what she meant). I'm glad that she took this initiative (I hadn't double texted her nor asked her why she wasn't replying, but well, it basically took her 3 days to reply to my previous text). She still hasn't read my reply, though (which I sent as soon as I woke up, so a few hours later). It's been a day already (well 23 hours, but still). Now, I am thinking of sending her this text (maybe tonight):

"Hey (name), I hope that you are doing well! I don't know what you're going through but as I said yesterday, I am here if you need someone to talk to. You're a good friend, and I understand if you need space. Anyway, I'm looking forward to chatting and/or watching films again! Take care, (name) 😉"

So my online friend has been acting distant lately. Left me on read on Wednesday (though my message didn't really require a response tbh), then I sent another text on Thursday (about something unrelated). She replied on Friday, said that she had been busy lately (preparing stuff for the weekend because she was apparently going to some events). OK, fine. I reply to her on Friday, she replies exactly 24 hours later on Saturday. On Saturday, I reply again, then send another message (invitation to spend time together because we haven't done it in a few weeks). Still no response after 2 days. I told myself: "She'll not hear from me again 'till she texts me".

She texts me on the 3rd day and says "Hey! I'm sorry, I haven't been feeling really good lately" (she didn't word it like that, but I guess that's pretty much what it meant). Then, she says that she hopes I'm feeling good and she asks me what I thought of the latest episode of the tv show that we both watch. She texted this very early in the morning, so I replied like 3 hours later (when I woke up). She still hasn't replied. But, we text on a website that doesn't send push notifications, so that might explain why she hasn't replied yet. But I don't want to check if she has read it (or else she'll see that I was active not long ago and probably believe that I'm obsessing over if she has read it or not). Saying this because she knows that I pretty much only chat with her on that website. I just don't understand, she literally apologized this morning for being inactive and now she's back at it again.

Anyway, now, my question is (please vote in the poll): should I stop texting her first and not double text as well (even if she might actually not be feeling all that good at the moment)? And should I ask her if she wishes to keep contact with me (could explain that I'm feeling a distance in the friendship)?