Is it true that if I start wearing glasses my eyesight will deteriorate?

No. However if you get used to wearing glasses and see better with them, then you'll want to wear them all the time and thus without them your eyes will seem worse (like deterioration). Glasses only correct a refractive error, not change the eyesight. Eyesight changes with a lot of near work without breaks, or with age as the cornea/lens changes, etc.
NO. This is a commonly held belief that is absolutely false. Wearing glasses will not make your eyesight deteriorate. If you need glasses, not wearing may make your site worse. You need to trust your eye care professional in this.