Brief Answer:
Related to muscle and/or tendon/ lipoma if long-standing

Detailed Answer:
Hi.
Thanks for your query and photos.
Noted the history, seen the photos.
Please give some additional information for me to assist you better:
Since when is the swelling present?
Any direct or indirect trauma due to some movement with some weight in hand?

Since there is no continuous pain, swelling is non-tender and not hard the most probable causes I can think about are as follows:
At times there is pain at some movements hence it can be due to muscle strain that has given the swelling.
Some inflammation due to myositis or tendinitis.
Lipoma or so if the swelling is of long-standing nature.
Infective pathology is a least possibility as there would have been pain, tenderness.
I would advise you the following:
Give rest to the affected parts, put the forearm in a sling.
Take some anti-inflammatory medicine like Ibuprofen.
See the results.

I hope this answers your query.
Please feel free to ask for further relevant queries if you feel that there is a gap of communication.

With Regards.
Dr T Chandrakant.
General Surgeon.

---