Just signed up for 3 months free Apple Music.Does the 3 month free Apple Music allow me to get songs for free from the iTunes Store to add to my Apple Music playlists? (usually they’re $1.29 each) i cant seem to escape the $1.29 charge no matter wh

There are two separate music libraries. The original is the iTunes Store, from which you can purchase songs to keep as long as you like. The Apple Music library is slightly smaller and is separately. As long as you pay the subscription you can stream any song in the library or download it for offline listening, and this comes at no further cost above the subscription: but if you stop the subscription these downloaded songs will disappear. Of course this does not affect any songs you've bought from the iTunes Store: you purchase these and they are not part of the Apple Music subscription.

You can still purchase music for a per-item fee through the iTunes store if you want. You retain rights to purchased music whether or not you have an active Apple Music subscription. But if you want to download music from Apple Music (without a fee) see: Add and download music and video content from the Apple Music catalog - Apple Support

You do not use the iTunes Store app to download Apple Music. If you download by using the iTunes Store app you are purchasing the music and you pay the price shown -- whether or not you have an Apple Music subscription. Some people want to do that in some cases because they want to own the music. If they downloaded it under Apple Music, they would only have the right to listen to it as long as they continued to subscribe.

If you want to download music that you are paying for with an Apple Music subscription, see the link previously supplied: Add and download music and video content from the Apple Music catalog - Apple Support

That link also states:

There's no cost to add or download content. Learn more about Apple Music and how to join. If you don't subscribe to Apple Music but want to download content to your device, you can buy music from the iTunes Store app on your iOS device or in iTunes on a Mac or PC.

What that doesn't say is that you can buy music from the iTunes Store app even if you are subscribed to Apple Music.

If you download using the iTunes Store app you pay. If you follow the instructions in Add and download music and video content from the Apple Music catalog - Apple Support

you don't pay.

You aren't alone. It seems that a lot of people only realize the difference AFTER they get a bill for downloading music that they thought was free.