Welcome to HCM
We understand your concerns
I went through your description. I suggest you not to worry much. Your wife was correct about the clear jelly like substance came out from your penis after pee. It is left over semen. Of course, mixed with some urine. This happens often. May be you noticed it just now. The burning you are worried about may be due to inflammation of the ureter
or nothing to worry at all. Just have plenty of water and you will see relief.
Hope this answers your query. Available for further clarifications.