What's the Difference Between the "Obsessed" and "Fixated"?

When talking about specific words as words instead of their meanings like you are here, you don’t need to say “the”. If you said “the”, then you would follow it with whatever “the” is referring to, whether it be a word, phrase or something else. So here you could also say “What’s the difference between the words “obsessed” and “fixated”?

I would appreciate it, if you could/would check out my example sentences.

“Could” would probably be the more common and also the more polite option.
The comma after “I would appreciate it” makes it feel like “if you could check out…” is starting a new idea which would also require more details. So with the comma, it makes the sentence feel kind of weird and empty in the sense that it’s missing some details.

I've been obsessed with making healthy desserts lately.

“Obsessed” implies that you’ve probably made more than one dessert, so it would become “desserts” in this case.

EspeciallyM's recipe in particular is my favorite.¶
OR¶
In particular, M'’s recipe is my favourite.

The original was right, but “especially”in this context feels a little unusual (to me at least).

What's the Difference Between the "Obsessed" and "Fixated"?

I would appreciate it, if you could check out my example sentences.

I've been obsessed with making healthy desserts lately.

Especially, M's recipeM's recipe especially is my favorite.

"Especially" usually doesn't come at the beginning of a sentence.

I've been fixated on her low-carb custard pudding, and ended up buying expensive sugar.

What's the Difference Between the "Obsessed" and "Fixated"?

"fixated" means focusing on one thing out of many, while "obsessed" means focusing on one thing so that nothing else matters.

I think "obsessed" is a little unhealthy; I often use it as a joke to exaggerate my dedication. (Like "I am obsessed with dark chocolate" xD)

I madhave some examples.

I would appreciate it, if you check out my example sentences.

I'm obsessed with studying English.

I've been obsessed with making healthy desserts lately.

I've been fixated on her low-carb custard pudding, and ended up buying expensive sugar.

What's the Difference Between the words "Obsessed" and "Fixated"?

I would appreciate it, if you could check out my example sentences.

When I come across an interesting new word, I tend to beget fixated on it.

"to be fixated on it" suggests you are already fixated when you come across the word, e.g "when I come across the word I am fixated on, I am very pleased to see it again".

"to get fixated on it" is better here because the word is new to you so at that point you become fixated on it.

I've been obsessed with making healthy desserts lately.

EspeciallyIn particular, M's recipe is my favorite.

as an adverb, "especially" attaches to a verb and joins it with another thing e.g:

I have lots of favourite recipes, especially M's.

I've been fixated on making her low-carb custard pudding, and ended up buying expensive sugar.

Your sentence is perfectly understandable, but "fixated on", when used figuratively like this, is usually applied to something more abstract, like a goal for example. If you say you are fixated on a physical object it implies you can't stop looking at it.

"I tried to have a meaningful conversation but I was fixated by her new necklace".