Might clindamycin be a strong enough antibiotic for a tooth abscess that has spread to my face and neck, and beyond?

Maybe. If this is the case, we recommend you be seen asap for an evaluation. Depending on when you started the antibiotic, you may already be behind the ability of an oral antibiotic to be effective and may need IV medication. Additionally, it may be necessary to drain the abscess in order to remove infection and allow the antibiotic to be effective. Thanks.
Yes and no. Clindamycin is a good antibiotic because of its accessibility to bone tissue in the cases of treating infection in bone. However, if your infection (tooth abscess) that has spread to face and neck even when you already taking Clindamycin for two to 3 days, i would see your dentist to establish a drainage. Too severe swelling(too much fluctuants) cause poor penetration of antibiotics to the site.
Possibly. But not the answer, you need to see a dentist, oral surgeon, or hospital asap. This type of infection is not something you fool around with by self medication and should be handled by a health care professional. Occasionally these types of infections can be life threatening if not treated properly.
EMERGENCY ! These situations need personal attention by trained health care professionals who can monitor the situation and treat you accordingly. This is not time to look for answers over the internet. These situations can become life threatening very quickly. See an oral surgeon or er doctor immediately.
It depends. For small abscesses and in case of allergies to penicillin is ok but in large spread infections to other areas a systemic combination of antibiotics wit drainage could be a better and faster solution see a dentist asap.