Given the information posted, I'm going to say that you're problem is a combination of things. Cheap skates with poor structure and support, causing you to have to tie them way too tight to get that support because you are a new skater. If they are not fitting you properly, that will compound the issue. Burning, cramping, pins and needles, or numbness are usually caused by too much pressure somewhere on the foot restricting blood flow. It may even not necessarily be in the area that is affected either. For example, pain or numbness on the outside of the sole (pinky toe side) is often caused by too much pressure over the top of the foot because that's where the blood vessel is.
IPv6 and others are correct. A skate should be supportive without having to crank it down. That relies on the thermoformability of the materials. Certain brands, like True or Easton Makos if you can find them, are made from materials that are a little softer and better shape to the foot. The higher price points from Bauer and CCM are made from materials that mold much better when heated. Doing what Vet88 suggests will definitely help you identify if pressure somewhere is the problem. It may be directly on the arch, it may not.
When it comes down to it, you're a new skater, so your strength and conrol aren't developed yet. You're likely having to crank the skate down just to get that support, since you don't have it on your own yet. Part of that may also be because the skate isn't fitting properly. And a cheaper boot doesn't have as much support, meaning you have to tie them even tighter to get it. I would take the suggestions of IPv6 and Vet88. Skate with your skates very loose and see if the lack of pressure resolves the issue. Don't worry about your skating, you're only focusing on the pain issue. If that helps, then I'm going to suggest finding a higher end boot, whether it's a True or another brand, that will provide its own support. To that end, I'm also going to suggest getting an ice skate and converting it to roller. Much of the price of a premade roller skate is in the wheels, bearings, and frame. You're getting a significanty inferior boot compared to the ice version of the same price point. A higher end boot on model year clearance or even used is a great option to consider. You already have the chassis, wheels, and bearings so converting over should be easy and not cost too much.