Red arm after immunisations

[BountyIsUnderrated]

Can I get an opinion on this, booster has not gone well for my relatives child.
Their whole upper arm has gone red and hot, she says its itchy.
Had the jab yesterday but its gotten worse and spread a bit since then, Dr prescribed antibiotics but said as she's not got a temp he thinks it's a reaction.
She now has a headache and has been crying she's sore so giving the antibiotics anyway.
Just wondering is this a common reaction?

Some people do get reactions. Have they tried an antihistamine?

Yeah also ibuprofen but it's not done much.
We think it could be a bad reaction but she had diarrhea and weed herself so going to keep a close eye on her.
If its a reaction it's a nasty one.