While I can understand your enthusiasm for resolving your workplace issues, bringing it up to your boss's private text messaging service on his cell phone was entirely inappropriate - to say nothing of badmouthing another employee on the same text line.

You are working in an IT profession, and information about your product is sensitive data, whether you think it is or not. That includes problems and resolutions to those problems. Information like this should be transferred via a secure medium, like your work email, rather than through personal texts.

These messages you sent to your boss now belong to him - they appeared on his cell phone after all - and he can indeed present them to HR if he so wishes. Be glad that you're only getting a warning for this type of conduct rather than dismissed entirely - exchanging sensitive work information like this is extremely dangerous.

That's not even bringing up the personal complaints about a co-worker, which should be addressed to your boss in-person or by work email even if you are not an IT professional, and only if you have already made an effort to resolve this personal conflict with your co-worker already.

The absolute best thing you can do in this situation is accept that you made a mistake, apologize for it, promise not to ever do anything like it again in the future, and then never do anything like that again in the future. That's the entire point of a warning, and if you ignore it or dismiss it, you'll be in more trouble than you already are. Accepting responsibility for mistakes made involving your workplace (including off-hours work-related communication) is a part of everyone's work cycle, and you must learn to own up to mistakes.

In short: A write-up for this kind of behavior is entirely justified, your boss does have the right to show the contents of your text to HR, and you should accept responsibility for this blunder and move on.