The pump is mainly used for penile rehabilitation (for which you don't need to use the rings). You should continue using it even if you have sex a different way, and it will be doing you some good in keeping the penis functioning, stretchable, etc.
If you want to use the pump for sex, then your technique with the rings may be wrong. It would be worth asking to attend a pump clinic (off-shoot of ED clinic but probably shorter waiting times) to have the pump demoed on you correctly. This doubles the chances of using it successfully at home afterwards.
However, many people don't find the pump very useful for sex, even though it is for penile rehab, preventing shortening, thinning, and fibrosis/Peyronie's disease.
The PDE5 inhibitors can all have the issue with swallowing or acid reflux in some people, because your esophageal muscles also use PDE5 to contract, so PDE5 inhibitors can interfere with swallowing. Sometimes a lower dose of Tadalafil is still enough to make erections work, but not interfere with swallowing.
This leaves the vasodilator drugs used directly on the penis, mostly Alprostadil based, plus Invicorp which is a different pair of drugs. These are injections, and less invasive but often less effective, the MUSE pellet and Vitaros cream. Also, unlike PDE5 inhibitors, they don't need working nerves or even sexual arousal, but because erections generated this way are not triggered by sexual arousal, they don't go away when you get bored with sex, but hang around until the drug disperses. The other issue with these products is they take it in turns to regularly go unavailable, so you may need to learn to use more than one of them.