I'm impatient of spending another year(s) saving a large down payment and I'm pretty sure my mortgage and student loans will hinder me from getting a good loan.

Some say it could hinder wholesaling because you are bound by the Realtor Code of Ethics at all times. 

Lenders only give a percentage of the rent toward “rental income” and having one break even or need feeding will hinder you going forward on the next one. 

If you're going to adjust the price due to the covid thing, think of a creative way to do that so you won't hinder your chances of a higher market rent in the future. ie, if normal rent is $1500 and you reduce it to $1200 to get it rented, how will you get it back to $1500 once the virus goes away?

As far as city regulations there are none that are hindering in the area Im looking at & I would look into HOA and not rent anywhere that has regulations that would be detrimental to my business plan.

Will having my license hinder my ability to pay referrals to non-license holders?

DON'T hinder your approach to investing based on where you happen to live or want to live. 

The license as nothing to your wholesaling, it only hinders it.

No one would intentionally do that, so no, buying more properties in most cases will not hinder your ability to get future loans.

In my opinion keep doing what you are doing until you can't because it is hindering your goals whatever they are.Good luck!