On both sides of my lips you can see sort of "pouches" or pocket of fat or is it muscle? What can be done? (photo)

That's because of the laxity and volume loss. The best option will be in person consultation and discuss the tightening/lifting procedure like Ultherapy or discuss fillers to take care of the area of concern. Hope it helps. 

Tightening of the skin with Fractora RF is easy and noticeable. If you've wasted money on thermage or ultherapy, then you will be pleased to see something that actually works.  It is Fractora RF and is so worth tightening up those saggy skin areas.

Thanks for your question and posting a photo. 
An in person evaluation would be needed to know for sure, but likely what you are referring to is a result of natural facial aging. As we age, three things in particular usually happen: decrease in the elasticity of skin, loss of facial volume (fat), and drop in the position of tissues- called ptosis. The troublesome area you may be referring to is likely a result of the last issue- the drop in position of facial tissues. It is likely due to fat that has dropped in position from your lower cheek down to outside your lips. 
Unfortunately, Botox or fillers are not likely to correct the problem. In order to treat tissues that have dropped, they should be repositioned back to where they should be- this requires surgery. A form of facelift may be appropriate for you. Seeing a qualified plastic surgeon will allow a full examination and a detailed, personalized treatment plan to be discussed with you. 
Best wishes, 
Rohit Jaiswal, MD
Plastic Surgeon 

Thanks for your question. The reason why you have this small pouch is skin laxity associated with volume loss in the mid face. This can be improved with combination treatments of HA dermal fillers, energy based skin tightening like Radiofreqency and silhouette soft threads. 

The "pouch" you are seeing adjacent to your mouth is related to volume loss and skin laxity. A combination of fillers and a skin tightening treatment (i.e. Thermage CPT or FLX) would give you a nice improvement without having to undergo surgery. 

Thank you for your question and for sharing your photo. In my opinion, the pocket of tissue you are referring to looks like the result of facial volume loss and skin laxity. There are many options available... from fillers like Restylane, and Voluma to help with volume loss and Sculptra, lasers, heat, Micro needling, PDO Threads etc to help promote collagen and skin tightening/lift. I would recommend an in person consult with a physician to fully assess and determine the best course for you.