Hi, My Partner Has Got A Secondery Infection On He's

Hi, my partner has got a secondery infection on he's foot caused by athletes foot, we went to a walk in earlier and he has been prescribed antibiotics.. he relised he has a bright red line on he's right arm going down to he's shoulder.. what could this be? Could it be related to the infection on he's foot even tho it's he's left foot what has the infection?