Oh I used to be like this too, until I realized that I sometimes don't reply to texts either. After realizing this, I actually began to calm down a bit when it came to people not replying. I rationalized that if I don't always reply, then other people can sometimes not reply as well. Also, I tried thinking of reasons why I don't like replying and just thought positively that maybe other people have the same reasons to why they don't reply.
So first reason I came up with was because sometimes I don't know what to say. Sometimes, certain texts messages leaves you hanging. When getting those texts, you can't really reply to them. And if somehow you manage to, it'll probably sound confusing, hurtful, and/or odd. Maybe it hasn't happened to you yet, but other people know what I'm talking about. So it could possibly be that some of your text messages are hard to reply to and people just choose not to do it since it's so difficult.
Second reason is that they are busy. When I'm busy, I don't always reply. I may reply EVENTUALLY but not at the moment. For instance, I could be in the middle of a text conversation with someone as I'm going to school. In school, cell phones should not be in use, so I turn my off or stick it in my locker, thus I can't reply. I'm too busy with school and other stuff to even bother. Another example is when my dad decides to give me one of his long lectures. It's rude if I start texting while he's talking, so I refrain myself from doing so. And occasionally I fall asleep while I'm texting. You can't really reply when you're sleeping, can you? And when I wake up, the conversation has already passed over too long of a period that it is no longer relevant to reply in my mind. So maybe the people you are texting to are busy and can't always have time to reply.
A third reason is that they just don't care. I'm not saying that all the people you text are like this, but occasionally they're just not interested in the certain topic that you're discussing. My friends sometimes do this to me and I am also well aware that I do this to them too. It doesn't mean that I hate them or that they hate me; it simply means that their minds or my mind are on other things and not into what you're saying. If they actually hated you, they probably wouldn't even be texting you in the first place or send you some rude comment back. Not replying because they're disinterested only happens with my friends once in a while, but happens more often with people who actually don't really care or like me but at the same time don't dislike me (essentially acquaintances). So be aware of when this happens and who this happens with and keep track of it. For instance, if Person A does this to you often, then that just shows you that you aren't as close to Person A as you thought and you should either not bother with them or get to know them better.
Fourth reason: They don't feel like they need to reply. It's not because they can't or that they don't like you, it's because they felt the conversation has ended and there is nothing more to it. They could also feel that replying back at that very moment is irrelevant. Like when you shoot a text that says "if you need any help, let me know." People are generally going to think either replying an "okay, sounds good" or not reply at all because they don't need any help at the moment. So it's possible that you send messages like that and people just don't feel like they should reply. This ties in very closely to the first reason.
Lastly, it could be because they don't want to bother you. Maybe you were saying how you were doing such and such and they think that they are bothering you by texting you. Although I don't see this happening much with other people, I know that I do that. I'm considerate about other people's situations sometimes and realize that texting them does no good and I should probably leave them alone.
I believe the reason why you feel this way and why I felt that way for a very long time is because of fear that they don't like you. You may think that if they're not responding, it could mean that they dislike your company. Although that can be true in certain cases, it's highly unlikely in most, especially if you have texted each other before. I know that it's hard to get over this, but it is possible. It's just a form of paranoia and I'm sure that you're not the only one who feels this way. So like I said, just list out positive or neutral sounding reasons on why people don't always reply or think about reasons why you sometimes don't reply (unless you're the kind who ALWAYS replies). And apply those good reasons to others when they aren't replying back instead of worrying that they don't like you anymore or think you're an idiot. These reasons are usually the most reasonable as well as the most likely.
Anyway, I wish you luck on this. I hope that you will be able to calm this down a bit. I'll tell you that I'm not fully calmed down, but it has reduced significantly since I started thinking about reasonable reasons to not reply. I suggest giving that a shot!