I don't know the reactions of pyrite but found this paper: https://www.mdpi.com/1996-1944/15/12/4181/html which suggests the product of oxidation of pyrite with nitric acid may be FeSO4 and elemental sulphur:
FeS2(s) + 8 HNO3(aq) → Fe2+(aq) + SO42−(aq) + S0(s) + 8 NO2(g) + 4 H2O(aq)
But the way you are going about this is not very scientific - and not at all safe, as you have now found out. Why are you adding "bleach" and what is the chemistry of this bleach? Doing that is not going to help you determine what is in your yellow or reddish solution, is it? I think you need to weigh the quantities and calculate how much nitric acid to add, knowing its concentration, then test the resulting solution with pH paper before going any further. Then think about what else you might test for to see what is present. If you have excess acid and you start chucking in NaOH, or something nitric acid can decompose (like the hypochlorite often used in bleaches), you are asking for a trip to hospital. Eyesight is a precious thing.
It's great you are having fun with chemistry but please take care. Test with small quantities, in vessels with wide necks (not a graduated cylinder), so any sudden evolution of gas or heat can escape and with plenty of ventilation or in the open air if you are trying this at home. Gloves, face protection and long sleeves strongly recommended, as you say.