kat, i know how you feel.
i had a really awful time breastfeeding my first baby. i started mixed feeding him and expressing rather than direct feeding when he was 4.5 months.
I never got him back to the breast and eventually stopped expressing at 6 months
5 years on, i still feel guilty. i regret not pushing for more help, for not feeling like i COULD push for more help, for giving up
but you know what, he is a happy, healthy boy now. in fact, he is healthier than my 2 subsequent exclusively breastfed babies who both have egg/dairy intolerances!!
i think you just have to try and remember that you did what you felt was right at the time.
hindsight is a wonderful thing, but we CAN'T change the past, so we have to learn to live with it. you fed your baby for 4 weeks yes? that's far more than a lot of babies get and every single breastfeed makes a difference. she got the colostrum which is so important, she got that early bonding and closeness with you... you gave her the BEST start in life that you could.
yeah, it ended sooner than you would have liked, but it's ok. it really is