You re more likely to be able to tighten up a loose squeaky hardwood floor if you can get underneath it.
Can you fix floor from underneath.
But as you suspected you need to be very careful both with screw length selection and how deep you drive the screw so that you don t go too far up and come through the subfloor into the linoleum.
For squeaky floor repair begin from underneath the floor if you can.
This could mean bringing a flashlight into the basement cutting some drywall from the ceiling.
If the underside is covered you will have to work from above.
Separate wooden bridging members to eliminate noise problems.
If there is no movement when looking underneath at the subfloor then this may mean the finish floor is loose and needs to be pulled down with screws.
Nail the 2 4 to the joist.
To fix a floor covered with deep pile carpet drive a wallboard screw through the carpet and pad into the floor joist.
Repeat on the other side of this joist.
With hardwood floors drive ring shank or cement coated flooring nails into the seams between boards.
It helps if one person stands on the top of the floor walking or jumping while the other is locating the gap causing the noise.
If you have the ability the easiest thing to do is to get a look at your subfloor from underneath.
Using shims or packers to fill gaps between can be a quick and effective fix.
If you have enough crawling space underneath your floor you might spot spaces between the sub flooring and the joist.