I do not recall seeing any indication of the two being linked
Actually they are. In the visual novel, in Akiha's Route, what really happened when Shiki collpased is revealed. SHIKI inverted and attacked Akiha but Shiki protected her and died; however, Akiha gave up some of her life force to save Shiki.
She was outside playing with Shiki, her adopted brother, and her real brother, also named SHIKI. But the Tohno blood was much stronger in her real brother and he inverted to his non-human form. In this uncontrollable state, he lost control of himself and attempted to attack Akiha. Shiki jumped in the way to protect her and took the full force of the attack. Shiki died protecting Akiha, but Akiha used powers granted to her by her non-human blood to give him half of her life, allowing him to survive.
Source: Akiha Tohno - Personality (2nd Paragraph)
Akiha's pained expression is most likely from the strain of maintaining Shiki's
life alongside resisting the Inversion Impulse of the Tohno Demon Blood inside her, which she requires Kohaku's help for.
Akiha often struggles to maintain control over her Tohno blood and resisting her Inversion Impulse, which she has difficulty with due to her also maintaining Shiki's life, to the point she also had to drink Kohaku’s blood.
Source: Akiha Tohno - Personality (3rd Paragraph)
In her route however, it becomes too much as she succumbs to her Inversion Impulse in the end. In the True End of her route:
[Shiki] decides to kill himself instead (so that she will regain the life energy she gave Shiki when he died eight years ago, and then will be restored to her full strength so she can more easily resist her Tohno blood impulses and restore her mind).
Source: Akiha Tohno - Role - Akiha's Roue (8th Paragraph)
Suffice to say that there is more to the True Ending than what I have quoted, which you can read up on the site in the quoted paragraphs and those that follow.