Can I merge 2 forms into 1?

For example, I'd like to create individual forms to collect information from clients with specific health conditions but I'd also like the ability to provide a 2nd form (minus their contact info that they provided on the first form) if the client then says they also have a 2nd health condition.  I'd like this 2nd condition form to appear asking only required info and not all of the contact info they've already created, then hitting submit and everything would come to me electronically.

You can redirect your user from one form to another with conditional logic Change "Thank you" page: https://www.jotform.com/help/317-Change-Thank-you-URL-Based-on-a-Condition 

For example at the bottom of you first form you can ask your user if they have 2nd health condition and if they want to fill another form. If they select Yes you can redirect them to your other form, if they select No you can redirect them to Thank you page. 

On your second form you can leave only for example Full Name field, this way you will know which user submitted your form. Later you can combine submissions from both forms with this app: http://apps.jotform.com/app/combine_submissions 

Other possible way is to have questions related to 2nd health condition on your first form. You can show that question only if user has 2nd health condition. You can achieve that with Hide/Show fields conditional logic.

https://www.jotform.com/help/316-How-to-Show-or-Hide-Fields-Base-on-User-s-Answer 

https://www.jotform.com/help/196-Hide-or-Show-Multiple-Fields-at-Once 

Third possible solution would be to pass contact info that you user filled on the first form to your second form. 

https://www.jotform.com/help/351-How-to-Automatically-Pass-Form-Data-to-Another-Form 

Hope this will help. Let us know if you need further assistance.