Can I be fired for being sick?

You cannot be fired if--
1) You had and used paid time off (PTO) for any absence; or
2) You complied 100% with any company "call out" or "call in" policy for absences, including in terms of notice you provided, how many days you could take, and any documentation you had to provide (but note: not all companies have such policies; it is voluntary for them to let you call out/call in); or 
3) Your employer was coverd by the Family and Medical Leave Act or FMLA (had at least 50 employees working within a 75-mile radius), you were eligible for FMLA (had worked there at least a year and at least 1,250 hours in the last 12 months), and your need for leave came from a provable serious medical condition.
If fired despite 1), 2), or 3), that was wrongful termination, and you could try contacting the department of labor, who may be able to help you, or else consulting with an employment law attorney about suing for compensation and/or reinstatement.
If you missed work without doing any of 1) to 3) above, however, you could fired for absenteesim: you cannot miss work, even for medical reasons, without using PTO, adhering to your employer's voluntary call out policy (if it has one), or using FMLA leave. If you miss work when you legally may not, as stated, you may be terminated for absenteeism, which would be termination "for cause" which would make you ineligible for unemployment.
If you are now over the illness, you would not be able to now get disability.

You cannot be fired if--
1) You had and used paid time off (PTO) for any absence; or
2) You complied 100% with any company "call out" or "call in" policy for absences, including in terms of notice you provided, how many days you could take, and any documentation you had to provide (but note: not all companies have such policies; it is voluntary for them to let you call out/call in); or 
3) Your employer was coverd by the Family and Medical Leave Act or FMLA (had at least 50 employees working within a 75-mile radius), you were eligible for FMLA (had worked there at least a year and at least 1,250 hours in the last 12 months), and your need for leave came from a provable serious medical condition.
If fired despite 1), 2), or 3), that was wrongful termination, and you could try contacting the department of labor, who may be able to help you, or else consulting with an employment law attorney about suing for compensation and/or reinstatement.
If you missed work without doing any of 1) to 3) above, however, you could fired for absenteesim: you cannot miss work, even for medical reasons, without using PTO, adhering to your employer's voluntary call out policy (if it has one), or using FMLA leave. If you miss work when you legally may not, as stated, you may be terminated for absenteeism, which would be termination "for cause" which would make you ineligible for unemployment.
If you are now over the illness, you would not be able to now get disability.