My orthodontic retainer really hurts my teeth. Is this normal?

No. Retainers don't normally hurt the teeth unless you don't wear it for several days and the teeth move. You need to return to your orthodontist or dentist who made the retainer. They can determine the cause and make adjustments so it doesn't hurt.
No. If you haven't worn the retainer and allowed your teeth to shift slightly then your teeth will hurt or feel sore when you try to wear the retainer. If you have been the retainer your teeth shouldn't hurt. Please see your orthodontist for an evaluation.
New or year older. Are they new or more than a year old and are they clear or have metal wire in front? Tightness can be from not wearing them religiously and the teeth will move especially if the braces just came off. Teeth will move up to a year after braces are off and there's relapse of over 50% after 5-10 years. See your orthodontist and see if adjustments can be made and chk if teeth have started moving. .
No. A retainer holds teeth where they have been moved orthodontically. It should be a passive alliance. If something hurts, go back to your orthodontist to have retainer checked.
No. An orthodontic retainer should be passive and not put pressure on your teeth or gums. If you haven't worn it for a while and your teeth moved out of position it will not fit properly and would need to be adjusted or replaced.
Consistency matters. If you are inconsistent with your retainer wear, your teeth will wander a little at first and then more as you continue not wearing your retainer. I recommend wearing your retainer for a several weeks full time to reposition your teeth, this may require some advil (ibuprofen) to get through...As your teeth realign, the pressure reduces and you feel fine again. If this is not the issue, call your orthodonti.
Retainer. It may mean that your teeth have moved since your retainer was made. Not using the retainer regularly lets the teeth move and just a little movement can make your retainer too tight when you do wear it. See your orthodontist to make sure it is still the appropriate retainer for you. If you have a permanent retainer placed it may work better. Or it may not fit correctly - have it checked!