Gluing will temporarily solve this issue but in doing so will cause more of the same issues in other parts of the floor. If you intend on replacing the floor in the near future then go ahead. But if this floor is intending to stick around for awhile then gluing is not a good idea. How much clearance did you leave yourself around walls when it was installed?

Before glueless floating wood floors, you had to use a PVA type II adhesive, on the tongue or in the groove, and the use of strap clamps to compress, for a tight fit. Properly milled flooring capable of gluing t&G are still made. Not all engineered can be floated. Some have to sloppy of a T&G to do so. Those are usually gluedown only.

You already said that you can't glue down -- is that really true? I have a floating floor over cement and it's been fine, but I did have it laid by professionals.

Wow. Ok. Where to start. First and foremost the SHEET vinyl is the only one that can brag about water proof. If you have leaky pets or leaky people, this is the go-to product if water PROOF is a requirement. Sheet vinyl requires a professional install which is normally quite reasonable. The costs grow with the subfloor PREPARATION costs (where are a separate line item that may not have a "final total" until the job is complete). The click together vinyl planks are all the rage right now. Some are DIY friendly - but most are quite picky about technique and take +++patience to learn how to do it right without breaking the click-edge. It is possible to do this yourself....but it requires an understanding that you will have a STEEP learning curve. Be OK with that. The cost to install the planks is a little bit more than laminate flooring. Again the costs go much higher once subfloor preparation is added in. Again, this is a separate line item that, as above, might not have a final tally until the job is complete. The "flatness" quotient for vinyl planks is extremely important and can be considered outside the comfort zone of many long-term DIYers who have tackled several different projects. Again, it is possible to DIY....but it takes quite a bit of time to learn the skill/trade. A professional can have most of this done before you have figured out how to work the self-leveling-compound (which is not self-leveling BTW). Is there anything else that you were looking at for information? I've just touched on the two biggest differences between the two products. I didn't know how much info you were looking for.