Answers:
Both syphillis and chlamydia are curable infections, as are urinary tract infections.
So, someone who is HIV+ and acquire one of these infections can be treated and cured short much difficulty.
If the character's immune system is severely impair (they enjoy moved from self HIV+ to have AIDS) it can be more of a resist, but treatment is usually still significant.
None of it is fitting to hold. You can't receive rid of Syphillis and in attendance is no cure for HIV/AIDS even so. If you attain treated, gonorreah will go.