I will ignore the student visa bit and answer your real question, which is "Can I get a Canadian PR if I'm HIV+".
The answer is a bit complicated.
1. Yes, if you marry a Canadian citizen or Permanent Resident, then your HIV+ status will not render you inadmissible to Canada. This is probably not a practical option for you, but it is possible.
2. If you apply on your own (let's assume you qualify under Express Entry), then the answer is " it depends". You may get a PR if your condition is such that you won't be an excessive burden on the Canadian healthcare system. This will be determined by the medical exam. It will depend on the medication costs and other related health issues.
It's not impossible, but you can safely assume that it will be difficult.
This also affects your student permit - you have to go through a medical exam for that as well, and various other factors apply (which province you're going to, for one).
Many HIV+ applicants get accepted as long as they don’t have other costly medical conditions. You may have to switch medication regimens depending on the cost of your current treatment. Getting a student permit would be harder many of the insurance plans that are required for international students will refuse to insure people with expensive conditions, same as some provinces,