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In most cases the grey spot is the natural eye pigmentation.
Most of these are small clumps of pigment where the veins travel through the white of the eye (sclera) under the white layer there is a dark pigmented layer (choroid). Just have the pediatrician watch it. They tend to become less prominent as the child grows.
The hotness of the eyes maybe related to allergies, a viral infection or even early eye flu,
I would recommend talking to your pediatrician and getting her checked if the symptoms persist
Do get back for any clarifications
I would recommend talking to your pediatrician and getting her checked if the symptoms persist, you may give her a dose of tylenol at the present point of time if she feels feverish too,
Please get back for any clarification, do leave a positive feedback too,