I'll start with this: So many women, including myself, HAVE HAD THE MISFORTUNE of having had miserable sexual relationships with a man-child like you. Grow the fuck up and educate yourself for the next woman stumbles into your life, after this one hopefully dumps you, if you don't learn to please her.
Your inexperience could be excused, your selfishness CANNOT. She knows you have very little patience for her pleasure and needs. It's all about you. You're not really listening to her or asking her what works for her; she's having to ask you to care about her needs, as if it's a chore. She wouldn't just lie and say you're "not trying enough" if it weren't true. You're obviously not really paying attention when she does try to show you with her own hand. You're just, literally, going through the motions, moving your hand repetitively (maybe even too roughly which is why your hand's getting tired), just to say you tried. Poor little you.
Many women can't get aroused or get anywhere near orgasm if the guy is obviously annoyed or uninterested in doing what it takes to give her pleasure. She knows you're thinking she's taking too long and it makes her anxious, and then even less about to focus on any sensations, such as oral. That's precisely why she says she doesn't feel anything when you go down on her. She's probably unable to get out of her anxious head and into the sensations; or you don't know what you're doing because she doesn't want to tell you how. It's fine that you don't know how to please her orally, women are all different. She should feel free to tell you, but she knows you won't remember, because you're already impatient. My guess? You'll go down for a ridiculously short amount of time (less than 10 min, BTW avg time to come is longer for most women during oral), then complain that your:
You've probably already given her the idea that there's something wrong with HER, and not you. I'm sure she makes certain YOU always cum. Right? You've probably given her a complex which is very hard to shake for many women.
Did you know that almost all women need direct clitoral stimulation to have an orgasm? Or that almost all women require a minimum of 20 minutes of foreplay (Look that word up, since you obviously have no idea what it is) before they're even aroused enough for penetration? Hence, even if lubricated, some women find penetration painful if their vaginas haven't become engorged with blood aka erect (like a guy's erection, yes we get internal erections).
So, you admitted that just as she's finally about to come, you just gave up cause you're sweaty? Was your make-up running? Almost ALL women who get to the edge of an orgasm, whose lover then stops, lose almost all arousal, then the whole arousal process has to build up again. Question for you? How would you like it if, every time you were just about to come, she just stopped, and left you hanging? Great, huh? Obviously not, because later in your post, you say you got mad at her, cause she selfishly said it hurt and wanted to stop before you could get your rocks off. I can't even believe you admitted this. How did you get any upvotes? You deserve every harsh word.
This is repulsive-
"Last time she stopped me because it hurt, I got annoyed because I felt like we were just wasting time. I see her just a few days a month anyway. I wanted to cum and she made a weird face and started crying." W.T.F. is wrong with you?
She should dump you and find a decent grown-up man. But if she foolishly wastes another minute of her precious time on your ignorant ass, you need to read about foreplay, specifically for women, female genital anatomy and sexual response. Find it in yourself to give a fuck about learning to give her pleasure, learn to enjoy giving it, as much as receiving it. I'm sure she does. Women usually do. I do.
And file your goddamn nails. That is, file them, run them across the inside of your cheeks (the closest thing to her vaginal walls). If you feel zero edges, good job. If not, file some more.
Buy this book for yourself. You can't afford not to. It's a good start to learning how to give her oral.
"She Comes First: The Thinking Man's Guide to Pleasuring a Woman (Kerner)"
https://www.amazon.com/She-Comes-First-Thinking-Pleasuring/dp/0060538260
Buy this book for you and her to read together. It'll seem like you care.
"Come as You Are: The Surprising New Science that Will Transform Your Sex Life" (Nagoski)