Two different problems, each with possible solutions / ameliorating actions, based on personal experience of being at both ends of vaccination needles.
(1) Generally feeling awful - often people miss food and / or drinks in order to get a vaccination, so feeling ill might actually be, at least in part, dehydration - take food & a drink with you; a simple painkiller / antipyretic (brings down temperature) such as paracetamol can help with general feeling of illness / headache etc.
(2) Sore arm - often caused by holding arm too rigid when needle goes in; difficult, I know to relax, but if you hold hand on your hip, then let upper arm "flop", sticking out elbow, thay gives you the best chance of relaxing muscle.