That depends on what type(s) of "very deep psychological issues" you suspect yourself to have. I'd presume nothing good could come of giving LSD to a paranoid schizophrenic or someone afflicted with or genetically predisposed to any other type of psychosis.
From what I've read, around half of all schizophrenics have a substance use disorder. For example, cannabis, nicotine, and alcohol consumption and abuse is substantially higher amongst schizophrenics than the general population. One could argue that the drugs precipitated or spurred the disorder or that the drugs are used to assuage the symptoms of the disorder.
So, perhaps some drugs like nicotine possess salubrious effects for psychotics. But I cannot see how psychedelics stronger than, say, cannabis could not exacerbate the illness in the long run.
My advice is to try therapy and pharmacotherapy with FDA-approved drugs first and save self-medicating with recreational drugs as recourse if and only if the therapy and medications prove ineffective.
