oh OP - you sound very stressed.
By your own entry, your DF is worried about you and not an arse.
He may have been clumsy in his choice of words, but it sounds like he is trying to help - which lets face it, is difficult when things escalate into an argument.
When you are having a tough time in one area of your life, it's easy for this to 'bleed' into others and it becomes hard take an objective, rationale look at what's going on.
Take a few deep breaths.. and ask yourself if you have been more irritable at home than usual as a result of what's been happening to you at work.
If the answer is 'yes' - then you know you have something to work on. If it's 'no', then don't cut your dad out - calmly tell your dad that you don't like falling out with him, but that you disagree with his pov.
As for work, if you have HR department, go and talk to them about your concerns. That feels like a very scary step, but you shouldn't have to manage this situation without support.