My dog is having all kinds of problems

Question
I have a medium boxer mix breed who is having trouble breathing.  He has had recurring infections for about 6 months now.  He had a horrible infection from getting neutered.  He was debreeded and re-sutured.  Since then he has had these abscess looking spots popping up spontaneously.  One on his ear and under his tail, then one on his paw between the toes, then one on his eye (which has swollen it entirely shut), and now small bumps are felt under his fur around his neck and on his back.  Our vet has prescribed short supplies of antibiotics to treat each spot separately and has denied the possibility of these bumps being related.  Apollo is now taking an oral antibiotic as well as using an eye ointment.  Does it sound like we are throwing hundreds of dollars down the drain when we don't even have a diagnosis to the problem?  Our vet talked us out of doing a blood test because he thinks it is too expensive and the dog is just "clumsy" in his words.  Any suggestions?

Answer
Sincere apologies for the delayed response.

These widespread infections have me concerned that something is happening more systemic nature.  Have you noticed improvement with the oral antibiotics?

I would recommend bloodwork honestly to see if there is some problem in addition to or as a cause of the infection and to assess his immune system.  

I hope this helps.  Again apologies for the delay.