כשהייתי לחוצה, הדופק שלי היה מהיר יותר מהרגיל.

כש־ means when. It is a very common shortened form of כאשר.

So:

• כש־ = when
• הייתי = I was

Together, כשהייתי means when I was.

In everyday Hebrew, attaching כש־ directly to the next word is very normal.

הייתי is the 1st person singular past form of להיות (to be).

So:

• הייתי = I was
• היה = he/it was
• הייתה = she/it was

In this sentence, הייתי refers to the speaker: when I was...

Because לחוצה is feminine singular, and it agrees with the speaker.

• לחוץ = masculine singular
• לחוצה = feminine singular

So this sentence sounds like it is said by a female speaker.
If a male speaker said it, it would be:

כשהייתי לחוץ, הדופק שלי היה מהיר יותר מהרגיל.

The dictionary form is usually לחוץ.

Hebrew dictionaries typically list adjectives in the masculine singular form, even if the sentence uses a different form.

So:

• dictionary form: לחוץ
• feminine singular in the sentence: לחוצה

This word often means stressed, tense, or under pressure, depending on context.

Because the subject changes.

In כשהייתי לחוצה, the subject is I, so Hebrew uses הייתי = I was.

In הדופק שלי היה מהיר, the subject is הדופק שלי (my pulse), which is a masculine singular noun phrase, so Hebrew uses היה = was.

So the two past forms match two different subjects:

• הייתי = I was
• היה = it was / he was

Because מהיר agrees with הדופק, and דופק is a masculine singular noun.

So:

• דופק = masculine singular
• therefore מהיר = masculine singular adjective
• and היה is also masculine singular

Hebrew adjectives must agree with the noun they describe.

In Hebrew, possession with שלי often uses the definite article ה־ on the noun:

• הדופק שלי = my pulse
• literally: the pulse of mine

This is very natural Hebrew.

You may also encounter forms with possessive suffixes in more formal or literary language, but הדופק שלי is the normal everyday way to say it.

Exactly. In present tense, Hebrew usually does not use a separate word for am/is/are.

For example:

• הדופק שלי מהיר = my pulse is fast

But in the past and future, Hebrew does use forms of להיות:

• הדופק שלי היה מהיר = my pulse was fast
• הדופק שלי יהיה מהיר = my pulse will be fast

So היה is there because the sentence is in the past.

יותר means more, and Hebrew uses it to make comparisons.

So:

• מהיר = fast
• מהיר יותר = faster
  literally: fast more

This is the normal Hebrew way to form the comparative.

Then Hebrew adds מ־ before the thing being compared to:

• מהיר יותר מהרגיל = faster than usual

מהרגיל is made from:

• מ־ = than / from
• הרגיל = the usual / the normal

So מהרגיל literally means something like than the usual or than normal, and idiomatically it means than usual.

This is a very common Hebrew pattern:

• יותר מהרגיל = more than usual
• מהיר יותר מהרגיל = faster than usual

A natural pronunciation is roughly:

kshe-ha-YI-ti le-khu-TSA, ha-DO-fek she-LI ha-YA ma-HIR yo-TER me-ha-ra-GIL

A few helpful notes:

• כשהייתי often sounds like kshehayiti
• לחוצה has the stress on the last syllable: le-khu-TSA
• שלי = she-LI
• מהיר = ma-HIR
• יותר = yo-TER
• מהרגיל = me-ha-ra-GIL

As in most modern Hebrew words, the stress is usually on the final syllable.