Lots of parents with more than one child breastfed - I have four. Rather than having a negative effect on your DD, longer term it should be good for her to see her amazing Mum doing this amazing and natural thing for her brother.
But before I go any further, it is also fine to formula feed if you want to. Formula milk is not evil and there is nothing terrible in choosing to feed that way.
I think your mental health ma better deal with your choice to change to formula feeding if you embrace and own your own decision in doing it, rather than framing it with blame and fault.
Saying breastfeeding your DS "affecting my DD" is blaming her for the decision to stop breastfeeding. Rather than you just 'owning' the decision as a choice without assigning any blame or fault.
Likewise saying "bf is painful" is then framing yourself as to blame (why couldn't I do it when others manage). Again, better that it is no ones fault, no one is to blame.
Your future mental health may better cope with your choice is you just decide "I would prefer to formula feed", or "I don't want to breastfeed anymore" without justifying or making excuses. The excuses create the guilt.
Lots of people (your DD included, you will also be proud of yourself) are likely to be very proud of you if you manage to carry on breastfeeding, because it is hard work. BF mothers can be proud because they work through the hard times with feeding in a way formula feeding parents don't have to. There is a martyr element.
Equally no one will think less of you if you decide to formula feed. Formula milk isnt bad or evil. It is easy and covenient and often with a new baby easy and convenient is what you need, no need to be a martyr. It is your choice.
Make it less emotive. Like choosing to dress your child in a sleepsuit or dressing him in 'proper clothes' - this is a choice you make that carries no emotion, you just choose.
So remove the emotion from your choice of feeding and make the decision without creating false excuses that only make you feel guilty and nedlessly like a failure.
Choose to bottle feed. Choose to breast feed. Choose to mix feed. Its all good.