I have to prove that this transcript is only expressed in one location that different from other transcripts.

The short answer to this, is that you can't. Simply because it's very difficult to prove something in the negative. (e.g. that your transcript is NOT expressed in any other tissues).

If you restrict yourself to a panel of tissues, and avoid over-extrapolating, then you could show that your transcript is only in one particular tissue out of a panel of 5 or 10. This can be done using either bioinformatics or wet-lab work (preferably both in combination) depending on where you are strongest.

Bioinformatics - You would first need to check that your tissue of interest (e.g. eye in your above example) has a robust RNA-seq dataset. Align that data, check that your transcript is expressed in that tissue. Gather the data for your control tissues and repeat. Make sure that the depth of sequencing for each sample is comparable. You can identify individual transcripts with RNA seq, based on the exonic reads.

The human ENCODE and the GEO database will have all the public RNA-seq datasets.

Wet lab - Northern blot with a transcript-specific probe across a panel of tissues. A tried and tested technique with a billion references.