My nose and sinuses are congested and my head is spinning.

If you're describing a current, ongoing, uninterrupted state: yes, definitely. "my head spins" sounds more like it happens from time to time. Every couple of hours my head spins, but when I sit down it goes away.

But, I am not suffering much forbecause I am taking ibuprofen every now and then.

"for" is okay here but it's a very high-minded way to talk, like you're a character from a Victorian novel :)

Here "taking" and "take" are both okay, but "taking" is probably a bit more natural if you're talking about taking ibuprofen because of your current state. We kind of think of it as continuous, even though we aren't literally taking pills one after another. Because it's like a regular regimen, three hours ago I took ibuprofen, in another three hours I'll take some more, so even in the time between I'm still "taking" ibuprofen because I'm on that regimen. "I take ibuprofen" is more likely as a general description - whenever I get headaches I don't suffer much because I take ibuprofen.

As for suffer and suffering, I think "I'm not suffering" is a bit more natural but both are fine.

My days are uneventful and amI barely leavinge my bed.

Here present simple sounds better, but I'm not sure why. Continuous is possible but a bit strange. You missed an "I".

The diffuser is almost always on and I am inhaling eucaliyptus oil as much as possible.

Very similiar to the one about ibuprofen.

Other than that, I am mostly reading e-internet articles a. And I have picked up a new hobby -, knitting socks, which does not only activate my mind, but it is also very peaceful.

Never seen an English native say "e-articles", although it's super clear what you mean :)

This felt a bit odd as one sentence, and it also felt a bit odd to use the hyphen like that.

I am taking the meds prescribed by the doctor three times a day.

Again very similar to ibuprofen.

Besides, all I do is sleeping, drawing and playing games.

Or "the only things I do are sleeping..."

I am playing Minecraft and the League of Legends.

Sometimes I ham hanging out on FB with friends and I forget what I am living through.

Here we NEED present simple, I think. Because we explicitly mean sometimes, repeated events, not an ongoing thing. Continuous is possible if you cast it as more regular, "I'm hanging out on FB every night with my friends".

Would it also be correct to replace all those instances of the present continuous with the present simple, like with:

Describing how someone is spending their days during an illness

one is more poetic

But, I am not suffering much forbecause I am taking ibuprofen every now and then.

My days are uneventful and I am barely leaving my bed.