Am I stressing out my Leopard Gecko too much?

Welcome to GF and congrats on your new gecko. These geckos are a lot hardier than you would think and it's really ok (though hard for us) if they don't eat for quite awhile. Some of my geckos don't eat for weeks. They're not like mammals that need to eat every day. It's not unusual for a leopard gecko to refuse to eat when in a new place. If you have to move for a few days, I'd say, take him with you in his tank, so at least that will be familiar. Keep offering and try not to worry. He will eat eventually, most likely. A few notes about some of the details you presented:

Albino: I'm going to guess you're calling it albino because it's pretty much all white. However, if it's a "blizzard" which is a leopard gecko morph, it may not be albino at all. Google "blizzard leopard gecko"to see some pictures of what blizzards look like. There are albino blizzards, but unless you know for sure yours is also albino, it may be just a blizzard.

Activity: Just making sure you know that leopard geckos are nocturnal, so it's not unusual for them to sleep all day and be active at night

Temperatures/heat: It's usually best to provide heat with an under tank heater (and thermostat) that is kept on 24 hours. The temperature should be in the low 90's on the floor. I don't know if your measurement of 88 is in the air or on the floor.

Enjoy your gecko and don't hesitate to ask more questions.

Aliza

On the container it does say Blizzard Lizard (Albino) and was from a stand at the Exotic Pet Expo that sold geckos. When I goggle pictures of Blizzard Lizard and Albino Blizzard Lizard it looks closer to the Albino but I can't be quite sure.

As for the temperature, the thermometer is in the middle of the tank on the side with the heat source so his basking rock is above the ground up to the middle of the tank I was thinking that would be hitting that 88-90* F but once again I can't be sure

If the container said "albino" it's most likely an albino. I'm assuming the basking rock is not one that plugs in. If it is, it's not a good idea because they get too hot. If you have a thermometer that sticks on the wall and it's measuring that high, it means the air is 88-90 and that can get too hot for the gecko and dehydrate it. If you have a thermometer with a probe sitting on the floor (or on the rock) that's a good temperature but it would be nice if it could stay that warm at night as well (that's where the under tank heaters come in).

Aliza