Learn English – Sleepy tired vs physically tired

I'm trying to figure out if there is a better way to distinguish between being sleepy-tired, and being physically tired.

• Scenario A: You didn't get much sleep last night. It's only 10am so you've not done much today, but you keep nodding off. You are tired
• Scenario B: You've mowed the lawn, done a lot of heavy lifting, walked a lot, and now your muscles ache, you want to sit down. It's only lunchtime. You are physically tired, but wide awake. You are tired

I'm specifically asking about scenario B as you could use sleepy for Scenario A, which wouldn't get mixed up with physical tiredness.

I've looked at some synonyms such as exhausted and fatigued but I think these could also suggest some form of sleepiness.

I'm trying to find a one word or short way of saying "I'm tired, but not in the sleepy sense of the word" (*I'm physically tired, not sleepy tired)

I'm not asking for a way to say "It's bedtime, and although physically tired I'm still not sleepy"

The conversation scenario I'm trying to avoid:

A: sits down on the sofa, 8pm. "Boy, am I tired"

B: "well that's because you didn't have much sleep last night"

A: "No, I mean I'm physically tired, I'm actually not sleepy at all"

Is there a word A could initially use to avoid the sleep branch of the conversation? Does A have to resort to saying "Boy, I'm physically tired, but wide awake"?

Here's maybe a better way of what I'm driving at.

You didn't get much sleep during the night. You go to a long gym session at 9am and do more than you usually might, resulting in your muscles having a thorough workout. You have a coffee at 11am and then go home to your partner (who knows you didn't get much sleep) and flump on the sofa:

• You are physically tired (you just want to sit down as your muscles are tired)
• You've recovered from your immediate exertion (so you're not out of breath)
• You are mentally awake (You're ready to sit down and do the crossword)
• You don't feel sleepy at all (You could go to bed, but you wouldn't sleep. Why would you, it's the middle of the day and you've only just got up – you are not restless)

You want a short way to say "Phew, I'm tired!" but in a way that cannot be construed as being mentally tired or feeling the need for sleep. (and without having to qualify it with a longer sentence).