It’s possible that some STI/HIV can pass this way if it was done soon after someone had used the tampon applicator. It would be a similar chance of passing an STI if a sex toy was shared.
Most STI including HIV do not survive well when they are out of the body. This means it will be hard to know the exact risk as you do not know if the person has an STI or how long the applicator had been sitting there.
As this happened when you were a child any future STI testing would have picked this up. If you have never had an STI/HIV test it may be worthwhile going for a test.
Let us know if you have any more questions or concerns.