BLUE TONGUE SKINKS

I have a 6-7 month old skink who just finished his first brumation a couple days ago. While I'm happy it's finally over, he seems to have developed a possible RI (Wheezing/whistling). I haven't seen any other signs, aside from his breathing, but I plan on calling the vets in my city tomorrow morning to try and get him in to be checked on sometime within the next week. I also plan on getting his nails trimmed there, if possible. My main question is what should I put him in in order to be safely moved to the vet? It is winter time and he is relatively new to handling (only starting to calm down with handling after brumating), so I want to keep the experience as stressless as possible. Lastly, his nose seems to be a bit redder than the surrounding areas, is this a possible sign of something else?

My temps n humidity
Humidity: 30-40%
Basking: 90-95 (house got a bit colder from winter so its not quite at 100)
Cool side: ~75
Night: 65-70 (Looking into getting a low wattage heat emitter on a thermostat to raise the temps a bit)

A medium sized clikclak style tube ( a 35L or larger tub should be large enough for a full grown BTS) , or a small dog carrier or cat carrier .

Line it with an old bath towel.

Use an electric soldering iron to make air holes either in each end or each end of the lid to allow ventilation in the tube.

I'm guessing you'll be travelling by car? If so, I'd recommend heating up the car before getting them in there to get ambient temperature at a good level (though presume won't be as easy on the way back). The easiest would be to add a blanket in the carrier (both for grip and for them to hide under), along with a hot water bottle directly under, on the outside the carrier/tub (I would only place the hot waterbottle under half of the carrier so they can choose which side to be on). I would presume the vet would be able to reheat it for the journey back. Alternatively, you can get reptile dedicated 'crackable' heat pads, like the ones people often use in gloves

If travelling alone, make sure the carrier/tub is very secure in case they move around. Maybe on the floor of the car, or using a seat-belt. If someone is joining, you can request them to hold onto it on their lap for additional body heat.

For my vet journey, I heat up a wool sock filled with rice in the small cardboard container I got him from plus a t-shirt to burrow in.

I actually have a small pet carrier made from canvas and fabric and thick padding on the inside should the situation present itself. I sometimes transport for breeding purposes and this works very well.

Yup small pet carrier with heat pad and fleece blankets. Keeps them nice and warm. I then cover the entire outside with a heavy towel and blanket.