No, you should be able to view them many times
You are also being careful in handling them

I would suggest first holding the dvd up to the light at an angle such that you can see the surface clearly
What you are looking for are any obvious scratches, imperfections, damage, or excess dust on the surface
I'm assuming you are playing these in either a stand alone player or one integral to a TV set ?
If so try playing the dvd in your pc or laptop assuming you have one and see if you get the same results , or at least try another player you believe to be in good working order

If you get the same results it's likely the disk may be damaged and a visual inspection may confirm this.
If your disk plays ok in different player then it may be the drive itself,if you suspect it may be,and want to confirm, take a dvd you aren't, concerned about losing and try it in the suspected faulty player and then go through the same process as above

Good luck