AST DPS

Basically I would like to know how to get more damage with my AST in savage instances.

No simple answer here. If you want some targeted help then you'll need to share some fflogs with us (the only one available currently is one where you died twice, not the best parse to go off of).

If you're keeping uptime on your dots and still not doing enough dps for your liking it boils down to healing as little as possible. This involves a lot of work with your co-healer, making sure you don't heal on top of each other. Further down the road it may also involve your dps/tanks doing the best they can to keep you from having to heal them (bloodbath, secondwind, etc.)
Unfortunately it's a bit hard to give advice for healers without looking at parses. Mostly because the healing dps rotation is pretty hard to screw up so issues have more to do with uptime.

Also worth noting that about 25% of AST DPS comes in the form of raid DPS through cards. That's where I would start. Making sure you pull cards on cooldown and use them properly.

I've already done sigma savage v1 v2 and in practice v3 and I made sure to hit everything I could but my data was not recorded in the fflogs

There isn't too much trick to doing higher DPS on AST as we don't have too much to use.

Basically only heal when it is necessary. This may take a lot of time and practice to learn how much you can let people's HP float and also situations where you can let Regens heal everyone up slowly because there is no incoming damage for a bit. You kinda have to learn the danger zones and know when people need to be topped off and when they don't.

Otherwise you need to keep Combust II on the boss, and spam Malefic III as much as possible.

Setup AoE Balance Cards whenever you can and make use of the buff on yourself by fitting in as much DPS while it is active as possible.

Any useless cards like Bole? Minor Arcana to try for Lord of Crowns for extra damage. Use sleeve draw with proper setups to get more cards like Balance or Spear to AoE hopefully, and any extra Lord of Crowns helps.

Earthly Star also does damage when it explodes so use it to hit the boss as well when possible. Try to use it strategically so that you also heal party wide damage while doing so.

Pretty much everything Mister and AmurT said.
In general as a healer, you want to get into the habit of healing only when you NEED to heal, and letting regens tick the party up rather than you wasting a GCD on Helios or such.

Rely heavily on your OGCDs to heal. Earthly Star is great for heavy raid wide damage, and Essential Dignity can get a tank up quick.
Everytime you're not healing, you should have your GCD moving with Malefic III and Combust.

Of course, also keep in mind that AST isn't capable of dishing out quite as much personal damage as a SCH or WHM