That''s nonsense if they tell you that. Not that I doubt you, but I can't imagine a clinic not taking you in. Unless you are asking them if they do the testing on site, in the office. None do.
Any, and I mean any Physician can give you a lab request for tests for diseases, blood chemistry, hormones etc.
You then take that requisition to a lab like lifelabs.ca. Then they draw some blood, get you to pee in a little jar and they run the tests. (Make sure. you don't pee just before your visit to the lab so you have something in your bladder
Create an online account on lifelabs.ca and look for a local lab. Either make an appointment or check the wait times and go to the most convenient place. (I find the best time to go in is the early afternoon because mornings are busy with tests that require fasting. With an account, you can check your own test results online.
Here's my advice:
1. Get cleaned up, shaved, wear decent clothes before you go in. No offence intended as I don't know you but I know that Emergency Rooms and Walk-In clinics DO make an immediate judgement on how you are going to be treated. Be polite.
2. Go to ANY Walk-In clinic and ask to see a Doctor. When they ask what you are there for, tell them you would prefer to speak to the Doctor privately. If they insist, tell them you are not feeling well and want to discuss having some bloodwork done.
3. Wait patiently to see the Doctor as there are people ahead who have waited.
4. Tell the Doctor you don't have a family Doctor (if true) , or that you do have one but are not comfortable to ask for a full panel of STD tests, including HIV, Hepatitis A, B and C. Tell him if you have been vaccinated against Hepatitis and if so, tell him you want to make sure you do in fact have immunity.. Hep A can require a booster shot from time to time. Even Hep B can. Tell the Doctor in advance that you had a bit of a wild weekend a week ago had unprotected sex with two girls. And that you are worried about the possibility of giving your partner any infection.
5. Ask about Gardasil 9 HPV vaccine, and Shingrix if you can afford the vaccines or have insurance. And if you think you can't afford it, think twice. I know a 22 yo girl who died from cervical cancer from getting HPV during her FIRST time having sex...and we all know about Michael Douglas and other men who have developed throat cancer from eating ONE pussy that had HPV. And don;'t get me going on the agony of shingles. I have a female friend who is a very healthy 62 and she recently got a mild case of shingles and she is in a lot of pain. (She had the first shingle vaccine 12 years ago when she turned 50. While her Doc said it probably helped lessen the symptoms of the outbreak, she strongly advised her to get the Shingrix vax in 6 months and her husband get Shingrix asap. I knew a RICH 68 yo guy who took his own life after 6 months of a bad case of shingles.
6. If you feel the Doctor is receptive and accomodating tell the Doc that you have been feeling lethargic for about six months, nothing specific, but that you haven't had a physical or simple blood work done in years (if true or however long) and ask him if you should get full blood tests including A1C (long term blood glucose levels) , cardiac markers, whatever vitamins, especially Vitamin D because most Canadians are Vitamin D deficient. (you will have to pay $50 for the Vit D test if you don't qualify for free test) Tell Doc you want to start taking vitamins and want to be responsible/careful and want to know your baseline vitamins. Ask for an Iron Study to see if you are low on iron. Kidney and liver function. If you feel comfortable, ask the Doctor if you could book a full "Physical Exam" so you can get a good picture of your health. Doctors like doing Physicals as they get paid much more than the $20-$30 or so they get for a regular, one health issue, office visit.
The issue with a Doctor ordering blood tests is that the Doctor has to be willing and available to follow up with the results, before they can (ethically) order blood tests. But even Walk-In clinic Doctors care about people or they wouldn't have gone into medicine.
Also, I understand that Walk-In clinics that are co-located with Pharmacies are much more helpful as the clinic is driven by pharmacy sales.
Good luck.