Ok, good. I think we are done. You can uninstall adwcleaner by starting it and clicking the uninstall button. The JRT icon just delete as well as the JRT folder @ C:/

Malwarebytes you can keep and use. Remember the free version must be updated manually and a scan started manually.

Yes you do need antivirus but the adware you had most likely was installed when you installed some other software. Pay attention to where you download software. There are many download portals that will bundle all kinds of "offers." Check my link below.

As far as AV goes: You only need one on your computer. Free versions are just as good as the paid versions. Try one out for a few days, if you like it-keep it. If not uninstall it and try another one. Free AV in no special order:

Avast
Avria
Comodo
AVG
Bitdefender

If all is good- then happy safe surfing out there.