Welcome to HCM.
This is very unlikely. I hope you would have used a fresh toilet paper only. So the spot may likely from your own body only. Probably Piles?.
Unless you used tissue paper or a tissue paper with blood stain which had not dried may likely to be infectious Otherwise no chance.
Your symptoms of sore mouth, head ache, lymph adenitis
, and joint pains
could occur with any type of viral fever
So you need not worry and have a check for HIV antibodies
after 3 months once and get yourself relaxed. If your are worry too much then you can go for HIV PCR which will become positive within 3-4 weeks.
Get out of your fear soon.