I own an upright freezer where I tried to drill a hole into the side wall. Unfortunately I hit one of the aluminium tubes that sit on the outside close to the metal frame of the freezer. Is there a way to fix it through welding or can I maybe put some plastic tubing in between and clamp it down?
You've already let out the magic smoke (refrigerant). It's not enough to just fix the tubing, you have to replace the refrigerant.
This isn't something you can do yourself. You'll have to call a refrigerator repair service that is qualified to work with refrigerant.
Note that the cost of repair may exceed the replacement cost of the freezer.