Welcome to the forum. Thanks for your question.
On one level, your concerns are well-founded. It is true that HIV transmission is enhanced in the presence of other inflammatory STDs like chlamydia, and it is conceivable that your partner's reported symptoms could be caused by HIV (the weight loss more than the rash). OTOH, heterosexually transmitted HIV is uncommon in Japan, and even in the highest risk circumstances -- unprotected sex, chlamydia or other STD, etc -- the odds are low for transmission of HIV during any particular episode of vaginal sex (usually 1 chance in 1,000 or even lower). In other words, it definitely is not "automatic" that HIV would be transmitted just because she had chlamydia and you caught it.
Perhaps most important, your negative RNA test at 10 days is very reassuring; the large majority (95% or more) of newly infected people would have positive results by that time. Of course you should go forward with your plan for definitive testing, but you can stay mellow in the meantime, confident that the result will be negative.
Any standard antibody blood test at 4 weeks will be fine (but I would recommend against the oral fluids test): the combination of negative RNA at 10 days and antibody at 4 weeks is 100% reliable. For a little extra jolt of reassurance, you could request a "duo" or "4th generation" test, i.e. for both HIV antibody and p24 antigen, which by itself (without the RNA test) is 100% reliable at that time.
As you may know, or will see if you ask around or keep reviewing various websites, most public health agencies and other experts will also recommend a final antibody test at 3 months. This truly isn't necessary, as explained in the thread below -- but since it's officially recommended, you may decide to do it.
http://www.medhelp.org/posts/show/1891685
And now a one-word mini-lecture for the future: Condoms!
I hope these comments have been helpful. Best wishes-- HHH, MD