I am sorry that your question was unanswered for long.
How big are the swelling/
Are they painful and tender?
Are your finger and thumb movements painful?
Following are the possibilites of diagnosis;
A) Tenosynovitis; it is inflammation of the tendon and tendon covering (synovium). It is treated as following;
1) Anti-inflammatory analgesics like Motrin / Advil for around 10-14 days.2) Brace (on fingers)3) Physical therapy4) Warm compresses5) Local analgesic patch / ointment / sprayThese are the initial modalities and if the swelling and tenderness does not respond than the further interventions would be required (called as deep electro therapies and done at physical therapy center);1) iontophoresis, phonophoresis2) electrical stimulation3) shock wave therapy4) local steroid shots
B) Ganglion or synovial cyst; This is fluid filled in the tendon sheath. This needs sometimes aspiration or minor surgery but can respond to deep electro therapies mentioned above.
Both of these condition do not need any emergency measures so you may seek appointment with your primary care physician in routine hours.
Please feel free for your follow up questions.