There are several different things that can cause the symptoms you have described. The first is a simple urinary tract infection. Your veterinarian can send a urine sample out to the lab (or read it in his/her office) to see if an infection is present. Sometimes it takes a long course of antibiotics to help. Since your pet has been on antibiotics and still has symptoms I am worried that something else could be going on. It is possible that he could have stones in his bladder causing an obstruction of his urethra thus causing him to strain and have blood clots in his urine. Worst case scenario he could have a mass in his bladder or in his urethra causing the straining and the blood clots. Since he is not able to urinate a good stream I would definitely recommend taking him to see your veterinarian again or getting a second opinion from another vet if yours will not do further testing.