small bumps all over body

[Islander1]

I am writing for a loved one who is incarcerated in a federal prison. The medical help available there is minimal and he is suffering from small itchy bumps all over his body. They are generally about 1mm in size. They itch, but are not a painful itch, as with scabies or shingles. When popped, there is white stuff that comes out, then clear liquid. Sometimes they scab. Sometimes the same bump will ooze white again. They are not clustered, and to not appear to be due to heat or reactions to food. This problem has been ongoing for months.
He is 53 years old, and in the last few months has increased his time outside as well as increased his exercise.
He was recently on amoxicillin, and due to something I have read about various possibilities, has also been on antihistamines.  We thought it might be due to high production of androgen.
He also has brown spots on his chest and front torso, shoulders.
There is also a 3rd type of bumps, on the outsides of the palms of his hands in groups that are crimson red and appear to be under the skin. These don't itch.

[Alicia3998]

Eczema

[Mayormio]

Maybe they are fordyce spots.