Right off the bat - don't use other people's salary as leverage. It's fine to compare to get an idea for how your compensation stacks up, but making that comparison with your employer will usually not go well. This other employee might be doing other work for the company that is incredibly important, or they might be doing nothing at all, but the managers will be aware either way. All you need to know is that if your coworker can make that much, then so can you with the right strategy.
Talking to your manager is absolutely the right course, but it's not the first step. When you go to them, you are going to be arguing that the value you provide to the company warrants higher compensation. To do that, you're going to want to document, document, document. Get daily counts of how many tickets you do, how many hours you work, any major projects or tickets you contributed to, and anything else you did that was above and beyond. The longer of a period of time you have this for, the better. Avoid directly documenting anything regarding your coworker's work (for example, writing how many tickets you did and how many tickets the person who is paid more did, to show that they did fewer).
Once it comes to an appropriate time to ask for a raise, such as on the 6 months mark or for you the 1 year mark, ask to meet with your manager, and present your case as to why you are a hard-working, consistent, loyal employee who deserves a raise. Bring up what you documented (don't just hand them a paper with everything written on it - speak to the points) as proof of your hard work. And at the end, ask for a raise that you can justify. 30% is a hard number to sell, but you can ask for whatever you want and they can say no. I'll say it again - do not bring up your coworker as justification for your raise
Even if you can't secure a raise that is satisfactory, this was still worth doing before you leave - you can compound the raise you got into a new job. Say you get a 10% raise - go interview for a new job elsewhere, and then when you're asked your salary, you get to say a 10% larger number. Then try to get another 10% on top of that from the new company as incentive to leave your current company. It will all come down to your negotiating skills, though.