If experts' advices come as the standard, no, you don't need to get tested for HIV. But be careful next time.
It wasn't injected into my body but it did go down deep (probably as deep as the vein). Do you think I am at risk? Do I need to test?
As long as the content hasn't been injected into your body, then you had no HIV risk, but otherwise get tested 3 months from then.
Whether it dies is a separate matter but once it comes to contact with the air, it will immediately become unable to infect a new host.