Not for me to diagnose but if you work full time, have children and deal with most of childcare when not at work, do not get enough sleep for a sustained period of time, have young children who play up that sounds exhausting!!
By all means go to gp if you think you have mental health issues and want treatment, but in the meantime perhaps doing practical thing to help with your situation may help alleviate your feelings. Your life sounds exhausting so Inwould think its normal to feel exhausted and struggle. There is a useful acronym
H hungry
A angry
L lonely
T tired
If any of above are an issue it says deal with that issue to stop you from halting!! So sounds like tiredness, rest, needing extra help with childcare would help ,your mood and emotions. Can you talk to your husband about how tired you are, what your needs are. About asking for a few nights where he gets up in night so you can sleep through. Or family to take over for a few hours at a weekend so you can rest up. Or pay for more help if possible with house and family- not always possible, but one option.
Gp can offer medication and short term counselling but if your practical situations do not change then you may still end up where you are. So trying to change what can be changed, or accepting how things are if alternate strategies not an option??
Can you book a chat with your HV.you say children play up at night so she may be able to offer a sounding board and strategies to help you and them.