It's not unusual, and prolly more commonplace to be sized down when fitting for ski boots, so finding a size 7 to be better would not be weird. If this works best and your toes aren;t bangin hard against the front of the boot, then that's perferrable.
Tight - tight is good as long as you don;t get more hot spots on the feet and the ball of the foot area and toes are not getting crunched - tight is good.
You know, there's no real easy way to help make boots fit better for a beginner, over the internet - especially rental. There's no way to know what condition the boots are in, they even vary from one boot to the next, in the same size based on the amount of use they've seen.
socks make a big diff.
using socks which are too thick and sqoochy will give the appearance of comfort when trying on, but after a brief time on the hill, will cause discomfort, for lots of reasons.
Try to use as light a pair of socks as possible
Often rental boots are not quite dry enough from the prior day or use. If the boots you;ve gotten seem damp at all inside, ask for another pair which should be dry. Wet is a no-no...
Don;t tuck anything inside the boot!
Try to wear ski/snowbd/snow pants which have an elastic 'snowcuff' in the lower leg opening. Even the cheapest bibs/pants usually have these snowcuffs...
Try to make sure your feet stay dry.
If you perspire a lot in the boots, bring an extra pr of socks and change mid-day.
Many 'local' shops (those off-mtn and in-town - your town or the mtn town) will take a little more time to 'fit' the rental better. If you find a type/size of rental boots you like, you can often 'reserve' that rental boot for your ski day. Having the consistenct of a rental boot which fits well for the entire season would have a HUGE effect on your enjoyment and progress.
When you;re ready to buy equipment - buy boots FIRST.
Shop around, try on a lot, try to find a shop and boot fitter whom you think is working well with you.
Then before you buy, go to the boot/fitter forum here and ask them questions about your possible purchase. Lots of questions. They're good guys and help steer you well.
hope your excitment for skiing become a long term addiction!