Tjyylli

There are couple of good suggestion already given to you. I will add my bit as well. I'd like to suggest the word actually.

Actually (adverb) _{Oxford Dictionary}

As the truth or facts of a situation; really.

That this situation continues and is actually getting worse is simply not good enough

So, your sentence can be rewritten as follows:

Your situation is, actually, more severe than mine.

I would use

literally

: in a way that uses the ordinary or primary meaning of a term or expression

// He took the remark literally.

Here's an example from Reverso.context.net:

"Don't take it literally. He is inclined to exaggerate."

According to Oxford English Dictionary:

In its standard use literally means
‘in a literal sense, as opposed to a non-literal or exaggerated sense’, as for example in
"I told him I never wanted to see him again, but I didn't expect him to take it literally."

Saying "your situation is, undoubtedly, more severe than mine" would mean that there is absolutely no doubt that your friend's situation is more severe than yours. The meaning of this adverb is pretty straightforward. It simply means without doubt or certainly. It's a very common, everyday word.

I would go with Unarguably (or inarguably, depending on your personal preference).

Your situation is unarguably more severe than mine.

Or, perhaps, Unquestionably.

Your situation is unquestionably more severe than mine.

I think I'd stick with unarguably, though; that sounds better to my ears.

I would use simply:

[Merriam-Webster]
1 a : without ambiguity : CLEARLY
1 b : without embellishment : PLAINLY
1 c : DIRECTLY, CANDIDLY
2 a : SOLELY, MERELY

// eats simply to keep alive

// simply cleaned it up and went to bed

— Garrison Keillor
2 b : REALLY, LITERALLY

// the concert was simply marvellous

—often used as an intensive

// simply crawling with geniuses

— F. Scott Fitzgerald

As you can see, there are a lot of synonyms for simply. Of those, I think that both clearly and plainly would also be good choices for your sentence.

You might want to use:

realistically

2. In a way that is accurate and true to life.

So, your sentence might be written as follows:

Your situation is, realistically, more severe than mine.

I would think that, in your particular usage, it would draw some similarities between the other person's situation and yours, but wouldn't try to benchmark the severeness of it.

I would use certainly or indeed.

Your situation is certainly more severe than mine.

Your situation is indeed more severe than mine.

But if adverbial phrases are okay with you, I'd opt for 'as it is'.

Your situation, as it is, is more severe than mine.

I would use definitely. With this, there is no exaggeration or "unexageration" as you say. It just is.

Your situation is definitely more severe than mine.

But if you are searching for a phrase, then I would go with without a doubt

Your situation is, without a doubt, more severe than mine.

Since they are used in everyday conversation, I feel that these would be best fit for many situations.

How about "Your situation is, I shit you not, more severe than mine"?

Urban Dictionary:

The expression means I am being honest.

When someone tells the truth about something usually unbelievable.

unexaggeratedly

First,

Your situation is, without exaggerating, more severe than mine.

means that your situation does not exaggerate. You want to make
yourself the subject of the exaggerating:

Your situation is, without my exaggerating, more severe than mine.

Now the only adverb that may replace the without clause without changing
the meaning of the sentence is

unexaggeratedly

The notion that this is not "formal" or not quite all right so long as
it is not in a dictionary is misguided.

Although I don't see them working well/at all in your sentence as written (with "is" being modified), understatedly, conservatively or (to the extent that it's a word), minimis/zingly could arguably qualify as antonyms of "exaggeratedly" (i.e., as synonyms of "unexaggeratedly") and possibly work ok in the following rewrite:

Your situation can be described, [even] conservatively/understatedly/minimis/zingly, as being more severe than mine.

(linked examples above from Pamphlet Architecture 29: Ambiguous spaces; Hemingway on War; and Ancient Indian Tradition & Mythology;: The Skanda-Purāṇa (pts. 1-15, 19), respectfully, all via Google Books)

Seriously

Your situation is, seriously, more severe than mine.

Also the informal word "legit", although listed in most dictionaries only as an adjective, is also used as an adverb. Being quite informal a dictionary probably should not be your guide on how it's commonly used, but Oxford Living Dictionaries and Wiktionary do list it as an adverb. In this case I guess it might be a flat adverb, like "safe" in "drive safe".

legit

adverb

(slang) Honestly; truly; seriously.

He legit thinks he can pass the test on zero sleep.

That legit scared the hell out of me.
Wiktionary

...

The word legit is used to mean 'literally' in utterances like 'I am legit going to fail this test'.
Working with English Grammar: An Introduction (2018)

Consider sincerely, from M-W

in a sincere or truthful way : with truth, genuineness, or straightforwardness

"Your situation is more severe than mine, sincerely." Or "Your situation is, sincerely, more severe than mine.". With a special pause/emphasis around the word.