Eu estou com sede desde o almoço.

In Brazilian Portuguese, many physical states are expressed with estar + com + noun, literally to be with something:

• estar com sede = to be thirsty
• estar com fome = to be hungry
• estar com sono = to be sleepy

Portuguese can also say ter sede (to have thirst), but estar com sede is usually the most natural in everyday speech.

Desde means since (starting point in time). In Portuguese, it’s common to use the present to talk about something that started in the past and continues now:

• Eu estou com sede desde o almoço. = I’ve been thirsty since lunch / I’ve had thirst since lunch.

English often uses the present perfect (I’ve been…), but Portuguese frequently stays with the present (estou).

Because do already means de + o.

• desde + o almoço → desde o almoço (no contraction is made)
• de + o almoço → do almoço (this contraction happens)

So desde do would be redundant/ungrammatical.

Portuguese often uses a definite article with meals in a general sense:

• o almoço = lunch (the lunch/that mealtime)
• o jantar, o café da manhã similarly

You can sometimes drop the article depending on style/region, but desde o almoço is very standard and natural.

By default, desde o almoço usually implies today’s lunch (the most recent lunch), because that’s the most relevant reference point. If you mean a different day, you typically specify it:

• desde o almoço de ontem = since yesterday’s lunch
• desde o almoço de domingo = since Sunday lunch

Desde is the most direct way to say since (a starting point). There are other structures, but they emphasize duration differently:

• Estou com sede desde o almoço. (since lunch; starting point)
• Estou com sede há horas. (for hours; duration)
• Faz horas que estou com sede. (it’s been hours that I’m thirsty)

They’re all possible, but they’re not identical in focus.

Desde usually means since and often implies the situation started then and continues up to now.
A partir de means starting from and can be more neutral/planned, often used for schedules or rules:

• A partir de amanhã, não como açúcar. = Starting tomorrow, I don’t eat sugar.
  For thirst here, desde o almoço is the natural choice.

A common Brazilian pronunciation is roughly:
eu is-TOU com SEH-je DEZ-ji u aL-MOH-su

In natural speech, desde o often links smoothly, sounding close to dez-jiu (the o can attach to the previous word).