I have been writing about not just one, but two females; sisters. I've toyed with different methods/persons in this, but it seems I've come to an obvious roadblock. I wouldn't call it "writer's block" because I haven't stopped writing. But I've been writing with the irking notion that something is very, very wrong. Its ok for me to explore my feminine side, but obviously I can't know how a woman thinks. I can't validly write in first person within the head of a female, at least not correctly. So, how do I proceed? I might need to go back and make drastic changes.
The best advice I received when I started writing male characters was to stop thinking of them as males and start thinking about them as people. It's not so much what's in the pants as how they've grown up: a male character whose father pushed him to be a tough guy and give up unmasculine persuits is going to be totally different than one whose parents supported his love of art or music. Ultimately, everything about a character is going to be shaped by either their innate personality or their life experiences - and that's going to provide far more variation between people than gender alone.
I don't think this is really a problem with the story being in first person. Regardless of the POV you use, you need to be able to really understand your characters, and you need to present that understanding in a way that feels genuine.
I think you need to decide whether there is something wrong, or if you just think there's something wrong. So, as John said, I'd get someone to read it for you. Preferably several someones, because, guess what? Women aren't monolithic. Every woman thinks differently.
So find out if there's a problem. If there isn't - if your betas tell you that they believed in the characters - excellent! Get back to work.
If there is a problem, try to get details on what it is, but also try to think of your characters as whole people. Yeah, okay, they're women, but what else are they? What has made them who they are? Their sex will have had more or less influence on their character depending on what society they grew up in, what their family was like, etc., but I don't think there's ever been a time or place where being female was all they would have been. Look at all of it, try to understand how it all fits together and influences everything else, and then try again.
Good luck with it!
It's good that you're thinking about it, because men and women generally do have different voices, different concerns, and different ways of approaching the world and its problems.
The key is whether you're paying attention to the characters you've created. Is one sister the peacemaker and the other one aggressive and ambitious? Then the ambitious one is not going to speak in the stereotypically soft, non-confrontational, consensus-building language which most women use. Unless, of course, you've set her up so that she's fighting that teaching, and that she wants to be blunt and forcible but is finding herself handicapped by her socialization.
Don't worry quite so much about the gender of your characters as their personality and capabilities. A nurturing man may tend towards chopping wood to make sure there's fuel for the fire, and a nurturing woman may bake bread. Conversely, a male psychologist who loves his family but who's not physically active may bake bread, and a farmer's wife who loves her family but doesn't know how to express her feelings may be the one out chopping wood.
Get beta readers, make sure they're of both genders, and ask them to pay attention to that aspect of the characters as they're reading.
ETA two books which may be useful to you to help you understand the difference between male and female thinking and communication: Deborah Tannen's You Just Don't Understand and John Gray's Men Are from Mars, Women are from Venus. Gray's book is relationship advice, but it's structured to explain one gender to the other.
Get a woman! Yeah, for proofreading, what did you think?
This irking notion is not so much different from all the other irking notions which assail your mind during writing.
If you write about a male politician, do you know how he feels and acts? Have you ever been a politician? How does it feel when the oppositions wants your head because of a wrong decision? Do you want to murder that journalist for asking this painful question again and again? Do politicians want to murder journalist at all?
What goes through the mind of a dragon, when this dingy two-legged mammal stands in front of him, waving a tooth-pick which with he wants to slaughter the fire-breather?
You make things up when you write. That's your job. And if you can write that passage about the dragon, then getting into a woman's head shouldn't be that different ;)
In your case you have the advantage, that you can ask other persons (test readers), male and female, if your characters work. That's more complicated with dragons. So embrace your easy challenge, keep writing, ask your test-readers, and slaughter dragons, that's so much fun. (Yeah, slaughtering politicians is even more fun. That's what the journalist is good for.)
I think that, as in relationships, if you focus too much on trying to figure out how their actions are defined by their gender, you won't be spending enough time on just getting to know the person as a person.
So does it help to get a woman to read it? Maybe. Or maybe it's better to get a married man to read it! Hard to say. No matter who you get, they need to be aware of the fact that not everyone thinks like them so they need to be careful with their feedback.
If you have a notion that something is wrong then your "block" is that the method you have chosen is frustrating you. Stop! You have found a way that you are not comfortable writing even if as you say you are still writing. You will do nothing more than get more frustrated.
If anyone suggested a definitive voice or approach to your issue you still might not be comfortable with that answer. Suppose I suggested third person for both characters and one printed in blue italics? Everyone said, "Yeah. That's the only way to do it!" YOU still have to be comfortable writing that way. It is subjective.
There are famous writers who've written first person as a person of another sex- Molly Bloom in Joyce's Ulysses comes to mind. He wrote it that way because he was comfortable writing it that way.