Might a popliteal aneurysm cause the upper leg to feel like it is pushing into the lower leg with general tightness in the knee and on the sides?

Yes!: Long and short of it: yes, a popliteal aneurysm could cause these symptoms.

Possibly: Popliteal aneurysms are a dangerous condition, as most do not cause symptoms until something catastrophic occurs; typically clots form in the aneurysm & embolize to the lower leg. This leads to emergent surgery & many times even with surgery the leg will be lost to amputation. The best way to diagnose is with ultrasound. Larger ones can be appreciated on leg exam. Sometimes tightness occurs.