Can I read runes for myself?
Yes. No old source knows a ban on reading for yourself: not the poems, not Tacitus. The idea that you must not comes from modern manuals, and they do not agree with one another about it either.
Where this comes from
oldest description Tacitus, Germania, chapter 10 · about AD 98
Tacitus describes the same lot-casting done publicly and at home, side by side. In the household form the head of the family reads the lots himself, for his own people. A ban on reading for yourself appears in no old text: it belongs to the modern manuals.
What the poems say
The poems say nothing about who may cast or read. They describe the runes, and a rune belongs to whoever learns it. What each rune means in them is gathered here, rune by rune.
The rune of the day: one rune, one question Do runes actually work? An honest answer